diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 95362521f3b9f..74d25d420e1a1 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -20,7 +20,7 @@ Other Enhancements
 ^^^^^^^^^^^^^^^^^^
 
 - :meth:`Timestamp.replace` now supports the ``fold`` argument to disambiguate DST transition times (:issue:`25017`)
--
+- :meth:`DataFrame.at_time` and :meth:`Series.at_time` now support :meth:`datetime.time` objects with timezones (:issue:`24043`)
 -
 
 .. _whatsnew_0250.api_breaking:
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index df91c71cfe238..5c591f3dd00ac 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -1302,20 +1302,19 @@ def indexer_at_time(self, time, asof=False):
         --------
         indexer_between_time, DataFrame.at_time
         """
-        from dateutil.parser import parse
-
         if asof:
             raise NotImplementedError("'asof' argument is not supported")
 
         if isinstance(time, compat.string_types):
+            from dateutil.parser import parse
             time = parse(time).time()
 
         if time.tzinfo:
-            # TODO
-            raise NotImplementedError("argument 'time' with timezone info is "
-                                      "not supported")
-
-        time_micros = self._get_time_micros()
+            if self.tz is None:
+                raise ValueError("Index must be timezone aware.")
+            time_micros = self.tz_convert(time.tzinfo)._get_time_micros()
+        else:
+            time_micros = self._get_time_micros()
         micros = _time_to_micros(time)
         return (micros == time_micros).nonzero()[0]
 
diff --git a/pandas/tests/frame/test_timeseries.py b/pandas/tests/frame/test_timeseries.py
index bc37317f72802..31e81a9ca77c2 100644
--- a/pandas/tests/frame/test_timeseries.py
+++ b/pandas/tests/frame/test_timeseries.py
@@ -6,6 +6,7 @@
 
 import numpy as np
 import pytest
+import pytz
 
 from pandas.compat import product
 
@@ -647,6 +648,28 @@ def test_at_time(self):
         rs = ts.at_time('16:00')
         assert len(rs) == 0
 
+    @pytest.mark.parametrize('hour', ['1:00', '1:00AM', time(1),
+                                      time(1, tzinfo=pytz.UTC)])
+    def test_at_time_errors(self, hour):
+        # GH 24043
+        dti = pd.date_range('2018', periods=3, freq='H')
+        df = pd.DataFrame(list(range(len(dti))), index=dti)
+        if getattr(hour, 'tzinfo', None) is None:
+            result = df.at_time(hour)
+            expected = df.iloc[1:2]
+            tm.assert_frame_equal(result, expected)
+        else:
+            with pytest.raises(ValueError, match="Index must be timezone"):
+                df.at_time(hour)
+
+    def test_at_time_tz(self):
+        # GH 24043
+        dti = pd.date_range('2018', periods=3, freq='H', tz='US/Pacific')
+        df = pd.DataFrame(list(range(len(dti))), index=dti)
+        result = df.at_time(time(4, tzinfo=pytz.timezone('US/Eastern')))
+        expected = df.iloc[1:2]
+        tm.assert_frame_equal(result, expected)
+
     def test_at_time_raises(self):
         # GH20725
         df = pd.DataFrame([[1, 2, 3], [4, 5, 6]])