diff --git a/src/compiler/core.ts b/src/compiler/core.ts
index 79b6249539dbc..8a2040a83df07 100644
--- a/src/compiler/core.ts
+++ b/src/compiler/core.ts
@@ -849,13 +849,22 @@ namespace ts {
     const extensionsToRemove = [".d.ts", ".ts", ".js", ".tsx", ".jsx"];
     export function removeFileExtension(path: string): string {
         for (const ext of extensionsToRemove) {
-            if (fileExtensionIs(path, ext)) {
-                return path.substr(0, path.length - ext.length);
+            const extensionless = tryRemoveExtension(path, ext);
+            if (extensionless !== undefined) {
+                return extensionless;
             }
         }
         return path;
     }
 
+    export function tryRemoveExtension(path: string, extension: string): string {
+        return fileExtensionIs(path, extension) ? path.substring(0, path.length - extension.length) : undefined;
+    }
+
+    export function isJsxOrTsxExtension(ext: string): boolean {
+        return ext === ".jsx" || ext === ".tsx";
+    }
+
     export interface ObjectAllocator {
         getNodeConstructor(): new (kind: SyntaxKind, pos?: number, end?: number) => Node;
         getSourceFileConstructor(): new (kind: SyntaxKind, pos?: number, end?: number) => SourceFile;
diff --git a/src/compiler/diagnosticMessages.json b/src/compiler/diagnosticMessages.json
index af8dd8ceb6971..373e5fc3388c1 100644
--- a/src/compiler/diagnosticMessages.json
+++ b/src/compiler/diagnosticMessages.json
@@ -2768,6 +2768,10 @@
         "category": "Error",
         "code": 6131
     },
+    "File name '{0}' has a '{1}' extension - stripping it": {
+        "category": "Message",
+        "code": 6132
+    },
 
     "Variable '{0}' implicitly has an '{1}' type.": {
         "category": "Error",
diff --git a/src/compiler/program.ts b/src/compiler/program.ts
index bab554927e726..5440b1a782b2d 100644
--- a/src/compiler/program.ts
+++ b/src/compiler/program.ts
@@ -619,8 +619,25 @@ namespace ts {
      * in cases when we know upfront that all load attempts will fail (because containing folder does not exists) however we still need to record all failed lookup locations.
      */
     function loadModuleFromFile(candidate: string, extensions: string[], failedLookupLocation: string[], onlyRecordFailures: boolean, state: ModuleResolutionState): string {
+        // First try to keep/add an extension: importing "./foo.ts" can be matched by a file "./foo.ts", and "./foo" by "./foo.d.ts"
+        const resolvedByAddingOrKeepingExtension = loadModuleFromFileWorker(candidate, extensions, failedLookupLocation, onlyRecordFailures, state);
+        if (resolvedByAddingOrKeepingExtension) {
+            return resolvedByAddingOrKeepingExtension;
+        }
+        // Then try stripping a ".js" or ".jsx" extension and replacing it with a TypeScript one, e.g. "./foo.js" can be matched by "./foo.ts" or "./foo.d.ts"
+        if (hasJavaScriptFileExtension(candidate)) {
+            const extensionless = removeFileExtension(candidate);
+            if (state.traceEnabled) {
+                const extension = candidate.substring(extensionless.length);
+                trace(state.host, Diagnostics.File_name_0_has_a_1_extension_stripping_it, candidate, extension);
+            }
+            return loadModuleFromFileWorker(extensionless, extensions, failedLookupLocation, onlyRecordFailures, state);
+        }
+    }
+
+    function loadModuleFromFileWorker(candidate: string, extensions: string[], failedLookupLocation: string[], onlyRecordFailures: boolean, state: ModuleResolutionState): string {
         if (!onlyRecordFailures) {
-            // check if containig folder exists - if it doesn't then just record failures for all supported extensions without disk probing
+            // check if containing folder exists - if it doesn't then just record failures for all supported extensions without disk probing
             const directory = getDirectoryPath(candidate);
             if (directory) {
                 onlyRecordFailures = !directoryProbablyExists(directory, state.host);
@@ -629,7 +646,7 @@ namespace ts {
         return forEach(extensions, tryLoad);
 
         function tryLoad(ext: string): string {
-            if (ext === ".tsx" && state.skipTsx) {
+            if (state.skipTsx && isJsxOrTsxExtension(ext)) {
                 return undefined;
             }
             const fileName = fileExtensionIs(candidate, ext) ? candidate : candidate + ext;
diff --git a/src/harness/harness.ts b/src/harness/harness.ts
index d6959c2a54fdd..56d66e753969b 100644
--- a/src/harness/harness.ts
+++ b/src/harness/harness.ts
@@ -1,7 +1,7 @@
 
 //
 // Copyright (c) Microsoft Corporation.  All rights reserved.
-// 
+//
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
 // You may obtain a copy of the License at
@@ -350,7 +350,7 @@ namespace Utils {
         assert.equal(node1.end, node2.end, "node1.end !== node2.end");
         assert.equal(node1.kind, node2.kind, "node1.kind !== node2.kind");
 
-        // call this on both nodes to ensure all propagated flags have been set (and thus can be 
+        // call this on both nodes to ensure all propagated flags have been set (and thus can be
         // compared).
         assert.equal(ts.containsParseError(node1), ts.containsParseError(node2));
         assert.equal(node1.flags, node2.flags, "node1.flags !== node2.flags");
@@ -751,7 +751,7 @@ namespace Harness {
         (emittedFile: string, emittedLine: number, emittedColumn: number, sourceFile: string, sourceLine: number, sourceColumn: number, sourceName: string): void;
     }
 
-    // Settings 
+    // Settings
     export let userSpecifiedRoot = "";
     export let lightMode = false;
 
@@ -790,7 +790,7 @@ namespace Harness {
             fileName: string,
             sourceText: string,
             languageVersion: ts.ScriptTarget) {
-            // We'll only assert invariants outside of light mode. 
+            // We'll only assert invariants outside of light mode.
             const shouldAssertInvariants = !Harness.lightMode;
 
             // Only set the parent nodes if we're asserting invariants.  We don't need them otherwise.
@@ -935,7 +935,7 @@ namespace Harness {
             libFiles?: string;
         }
 
-        // Additional options not already in ts.optionDeclarations 
+        // Additional options not already in ts.optionDeclarations
         const harnessOptionDeclarations: ts.CommandLineOption[] = [
             { name: "allowNonTsExtensions", type: "boolean" },
             { name: "useCaseSensitiveFileNames", type: "boolean" },
@@ -1187,7 +1187,7 @@ namespace Harness {
                 errLines.forEach(e => outputLines.push(e));
 
                 // do not count errors from lib.d.ts here, they are computed separately as numLibraryDiagnostics
-                // if lib.d.ts is explicitly included in input files and there are some errors in it (i.e. because of duplicate identifiers) 
+                // if lib.d.ts is explicitly included in input files and there are some errors in it (i.e. because of duplicate identifiers)
                 // then they will be added twice thus triggering 'total errors' assertion with condition
                 // 'totalErrorsReportedInNonLibraryFiles + numLibraryDiagnostics + numTest262HarnessDiagnostics, diagnostics.length
 
@@ -1497,7 +1497,7 @@ namespace Harness {
             };
             testUnitData.push(newTestFile2);
 
-            // unit tests always list files explicitly 
+            // unit tests always list files explicitly
             const parseConfigHost: ts.ParseConfigHost = {
                 readDirectory: (name) => []
             };
diff --git a/tests/baselines/reference/moduleResolutionWithExtensions.js b/tests/baselines/reference/moduleResolutionWithExtensions.js
new file mode 100644
index 0000000000000..df12a3531bcfa
--- /dev/null
+++ b/tests/baselines/reference/moduleResolutionWithExtensions.js
@@ -0,0 +1,46 @@
+//// [tests/cases/conformance/externalModules/moduleResolutionWithExtensions.ts] ////
+
+//// [a.ts]
+
+export default 0;
+
+// No extension: '.ts' added
+//// [b.ts]
+import a from './a';
+
+// Matching extension
+//// [c.ts]
+import a from './a.ts';
+
+// '.js' extension: stripped and replaced with '.ts'
+//// [d.ts]
+import a from './a.js';
+
+//// [jquery.d.ts]
+declare var x: number;
+export default x;
+
+// No extension: '.d.ts' added
+//// [jquery_user_1.ts]
+import j from "./jquery";
+
+// '.js' extension: stripped and replaced with '.d.ts'
+//// [jquery_user_1.ts]
+import j from "./jquery.js"
+
+
+//// [a.js]
+"use strict";
+exports.__esModule = true;
+exports["default"] = 0;
+// No extension: '.ts' added 
+//// [b.js]
+"use strict";
+// Matching extension 
+//// [c.js]
+"use strict";
+// '.js' extension: stripped and replaced with '.ts' 
+//// [d.js]
+"use strict";
+//// [jquery_user_1.js]
+"use strict";
diff --git a/tests/baselines/reference/moduleResolutionWithExtensions.symbols b/tests/baselines/reference/moduleResolutionWithExtensions.symbols
new file mode 100644
index 0000000000000..e9934946a64fd
--- /dev/null
+++ b/tests/baselines/reference/moduleResolutionWithExtensions.symbols
@@ -0,0 +1,37 @@
+=== /src/a.ts ===
+
+No type information for this code.export default 0;
+No type information for this code.
+No type information for this code.// No extension: '.ts' added
+No type information for this code.=== /src/b.ts ===
+import a from './a';
+>a : Symbol(a, Decl(b.ts, 0, 6))
+
+// Matching extension
+=== /src/c.ts ===
+import a from './a.ts';
+>a : Symbol(a, Decl(c.ts, 0, 6))
+
+// '.js' extension: stripped and replaced with '.ts'
+=== /src/d.ts ===
+import a from './a.js';
+>a : Symbol(a, Decl(d.ts, 0, 6))
+
+=== /src/jquery.d.ts ===
+declare var x: number;
+>x : Symbol(x, Decl(jquery.d.ts, 0, 11))
+
+export default x;
+>x : Symbol(x, Decl(jquery.d.ts, 0, 11))
+
+// No extension: '.d.ts' added
+=== /src/jquery_user_1.ts ===
+import j from "./jquery";
+>j : Symbol(j, Decl(jquery_user_1.ts, 0, 6))
+
+// '.js' extension: stripped and replaced with '.d.ts'
+=== /src/jquery_user_1.ts ===
+import j from "./jquery.js"
+>j : Symbol(j, Decl(jquery_user_1.ts, 0, 6))
+>j : Symbol(j, Decl(jquery_user_1.ts, 0, 6))
+
diff --git a/tests/baselines/reference/moduleResolutionWithExtensions.trace.json b/tests/baselines/reference/moduleResolutionWithExtensions.trace.json
new file mode 100644
index 0000000000000..6e6589d7c1f8a
--- /dev/null
+++ b/tests/baselines/reference/moduleResolutionWithExtensions.trace.json
@@ -0,0 +1,32 @@
+[
+    "======== Resolving module './a' from '/src/b.ts'. ========",
+    "Module resolution kind is not specified, using 'NodeJs'.",
+    "Loading module as file / folder, candidate module location '/src/a'.",
+    "File '/src/a.ts' exist - use it as a name resolution result.",
+    "======== Module name './a' was successfully resolved to '/src/a.ts'. ========",
+    "======== Resolving module './a.ts' from '/src/c.ts'. ========",
+    "Module resolution kind is not specified, using 'NodeJs'.",
+    "Loading module as file / folder, candidate module location '/src/a.ts'.",
+    "File '/src/a.ts' exist - use it as a name resolution result.",
+    "======== Module name './a.ts' was successfully resolved to '/src/a.ts'. ========",
+    "======== Resolving module './a.js' from '/src/d.ts'. ========",
+    "Module resolution kind is not specified, using 'NodeJs'.",
+    "Loading module as file / folder, candidate module location '/src/a.js'.",
+    "File '/src/a.js.ts' does not exist.",
+    "File '/src/a.js.tsx' does not exist.",
+    "File '/src/a.js.d.ts' does not exist.",
+    "File name '/src/a.js' has a '.js' extension - stripping it",
+    "File '/src/a.ts' exist - use it as a name resolution result.",
+    "======== Module name './a.js' was successfully resolved to '/src/a.ts'. ========",
+    "======== Resolving module './jquery.js' from '/src/jquery_user_1.ts'. ========",
+    "Module resolution kind is not specified, using 'NodeJs'.",
+    "Loading module as file / folder, candidate module location '/src/jquery.js'.",
+    "File '/src/jquery.js.ts' does not exist.",
+    "File '/src/jquery.js.tsx' does not exist.",
+    "File '/src/jquery.js.d.ts' does not exist.",
+    "File name '/src/jquery.js' has a '.js' extension - stripping it",
+    "File '/src/jquery.ts' does not exist.",
+    "File '/src/jquery.tsx' does not exist.",
+    "File '/src/jquery.d.ts' exist - use it as a name resolution result.",
+    "======== Module name './jquery.js' was successfully resolved to '/src/jquery.d.ts'. ========"
+]
\ No newline at end of file
diff --git a/tests/baselines/reference/moduleResolutionWithExtensions.types b/tests/baselines/reference/moduleResolutionWithExtensions.types
new file mode 100644
index 0000000000000..fbc0091ee3b95
--- /dev/null
+++ b/tests/baselines/reference/moduleResolutionWithExtensions.types
@@ -0,0 +1,37 @@
+=== /src/a.ts ===
+
+No type information for this code.export default 0;
+No type information for this code.
+No type information for this code.// No extension: '.ts' added
+No type information for this code.=== /src/b.ts ===
+import a from './a';
+>a : number
+
+// Matching extension
+=== /src/c.ts ===
+import a from './a.ts';
+>a : number
+
+// '.js' extension: stripped and replaced with '.ts'
+=== /src/d.ts ===
+import a from './a.js';
+>a : number
+
+=== /src/jquery.d.ts ===
+declare var x: number;
+>x : number
+
+export default x;
+>x : number
+
+// No extension: '.d.ts' added
+=== /src/jquery_user_1.ts ===
+import j from "./jquery";
+>j : number
+
+// '.js' extension: stripped and replaced with '.d.ts'
+=== /src/jquery_user_1.ts ===
+import j from "./jquery.js"
+>j : number
+>j : number
+
diff --git a/tests/baselines/reference/nameWithFileExtension.errors.txt b/tests/baselines/reference/nameWithFileExtension.errors.txt
deleted file mode 100644
index 2aa341271cddb..0000000000000
--- a/tests/baselines/reference/nameWithFileExtension.errors.txt
+++ /dev/null
@@ -1,12 +0,0 @@
-tests/cases/conformance/externalModules/foo_1.ts(1,22): error TS2307: Cannot find module './foo_0.js'.
-
-
-==== tests/cases/conformance/externalModules/foo_1.ts (1 errors) ====
-    import foo = require('./foo_0.js');
-                         ~~~~~~~~~~~~
-!!! error TS2307: Cannot find module './foo_0.js'.
-    var x = foo.foo + 42;
-    
-==== tests/cases/conformance/externalModules/foo_0.ts (0 errors) ====
-    export var foo = 42;
-    
\ No newline at end of file
diff --git a/tests/baselines/reference/nameWithFileExtension.js b/tests/baselines/reference/nameWithFileExtension.js
index 2d487ede24572..8a7506c2d4298 100644
--- a/tests/baselines/reference/nameWithFileExtension.js
+++ b/tests/baselines/reference/nameWithFileExtension.js
@@ -8,6 +8,9 @@ import foo = require('./foo_0.js');
 var x = foo.foo + 42;
 
 
+//// [foo_0.js]
+"use strict";
+exports.foo = 42;
 //// [foo_1.js]
 "use strict";
 var foo = require('./foo_0.js');
diff --git a/tests/baselines/reference/nameWithFileExtension.symbols b/tests/baselines/reference/nameWithFileExtension.symbols
new file mode 100644
index 0000000000000..61e6a768ea6aa
--- /dev/null
+++ b/tests/baselines/reference/nameWithFileExtension.symbols
@@ -0,0 +1,14 @@
+=== tests/cases/conformance/externalModules/foo_1.ts ===
+import foo = require('./foo_0.js');
+>foo : Symbol(foo, Decl(foo_1.ts, 0, 0))
+
+var x = foo.foo + 42;
+>x : Symbol(x, Decl(foo_1.ts, 1, 3))
+>foo.foo : Symbol(foo.foo, Decl(foo_0.ts, 0, 10))
+>foo : Symbol(foo, Decl(foo_1.ts, 0, 0))
+>foo : Symbol(foo.foo, Decl(foo_0.ts, 0, 10))
+
+=== tests/cases/conformance/externalModules/foo_0.ts ===
+export var foo = 42;
+>foo : Symbol(foo, Decl(foo_0.ts, 0, 10))
+
diff --git a/tests/baselines/reference/nameWithFileExtension.types b/tests/baselines/reference/nameWithFileExtension.types
new file mode 100644
index 0000000000000..a0fca3d456219
--- /dev/null
+++ b/tests/baselines/reference/nameWithFileExtension.types
@@ -0,0 +1,17 @@
+=== tests/cases/conformance/externalModules/foo_1.ts ===
+import foo = require('./foo_0.js');
+>foo : typeof foo
+
+var x = foo.foo + 42;
+>x : number
+>foo.foo + 42 : number
+>foo.foo : number
+>foo : typeof foo
+>foo : number
+>42 : number
+
+=== tests/cases/conformance/externalModules/foo_0.ts ===
+export var foo = 42;
+>foo : number
+>42 : number
+
diff --git a/tests/baselines/reference/project/cantFindTheModule/amd/cantFindTheModule.errors.txt b/tests/baselines/reference/project/cantFindTheModule/amd/cantFindTheModule.errors.txt
index 7c071fdc208c2..e9f8842d5cbb5 100644
--- a/tests/baselines/reference/project/cantFindTheModule/amd/cantFindTheModule.errors.txt
+++ b/tests/baselines/reference/project/cantFindTheModule/amd/cantFindTheModule.errors.txt
@@ -1,12 +1,12 @@
-decl.ts(1,26): error TS2307: Cannot find module './foo/bar.js'.
+decl.ts(1,26): error TS2307: Cannot find module './foo/bar.tx'.
 decl.ts(2,26): error TS2307: Cannot find module 'baz'.
 decl.ts(3,26): error TS2307: Cannot find module './baz'.
 
 
 ==== decl.ts (3 errors) ====
-    import modErr  = require("./foo/bar.js");
+    import modErr  = require("./foo/bar.tx");
                              ~~~~~~~~~~~~~~
-!!! error TS2307: Cannot find module './foo/bar.js'.
+!!! error TS2307: Cannot find module './foo/bar.tx'.
     import modErr1 = require("baz");
                              ~~~~~
 !!! error TS2307: Cannot find module 'baz'.
diff --git a/tests/baselines/reference/project/cantFindTheModule/node/cantFindTheModule.errors.txt b/tests/baselines/reference/project/cantFindTheModule/node/cantFindTheModule.errors.txt
index 7c071fdc208c2..e9f8842d5cbb5 100644
--- a/tests/baselines/reference/project/cantFindTheModule/node/cantFindTheModule.errors.txt
+++ b/tests/baselines/reference/project/cantFindTheModule/node/cantFindTheModule.errors.txt
@@ -1,12 +1,12 @@
-decl.ts(1,26): error TS2307: Cannot find module './foo/bar.js'.
+decl.ts(1,26): error TS2307: Cannot find module './foo/bar.tx'.
 decl.ts(2,26): error TS2307: Cannot find module 'baz'.
 decl.ts(3,26): error TS2307: Cannot find module './baz'.
 
 
 ==== decl.ts (3 errors) ====
-    import modErr  = require("./foo/bar.js");
+    import modErr  = require("./foo/bar.tx");
                              ~~~~~~~~~~~~~~
-!!! error TS2307: Cannot find module './foo/bar.js'.
+!!! error TS2307: Cannot find module './foo/bar.tx'.
     import modErr1 = require("baz");
                              ~~~~~
 !!! error TS2307: Cannot find module 'baz'.
diff --git a/tests/cases/conformance/externalModules/moduleResolutionWithExtensions.ts b/tests/cases/conformance/externalModules/moduleResolutionWithExtensions.ts
new file mode 100644
index 0000000000000..6ad3565862337
--- /dev/null
+++ b/tests/cases/conformance/externalModules/moduleResolutionWithExtensions.ts
@@ -0,0 +1,28 @@
+// @traceResolution: true
+
+// @Filename: /src/a.ts
+export default 0;
+
+// No extension: '.ts' added
+// @Filename: /src/b.ts
+import a from './a';
+
+// Matching extension
+// @Filename: /src/c.ts
+import a from './a.ts';
+
+// '.js' extension: stripped and replaced with '.ts'
+// @Filename: /src/d.ts
+import a from './a.js';
+
+// @Filename: /src/jquery.d.ts
+declare var x: number;
+export default x;
+
+// No extension: '.d.ts' added
+// @Filename: /src/jquery_user_1.ts
+import j from "./jquery";
+
+// '.js' extension: stripped and replaced with '.d.ts'
+// @Filename: /src/jquery_user_1.ts
+import j from "./jquery.js"
diff --git a/tests/cases/projects/NoModule/decl.ts b/tests/cases/projects/NoModule/decl.ts
index a8a29852ac267..064f777c5512e 100644
--- a/tests/cases/projects/NoModule/decl.ts
+++ b/tests/cases/projects/NoModule/decl.ts
@@ -1,4 +1,4 @@
-import modErr  = require("./foo/bar.js");
+import modErr  = require("./foo/bar.tx");
 import modErr1 = require("baz");
 import modErr2 = require("./baz");