diff --git a/Lib/test/test_typing.py b/Lib/test/test_typing.py
index e606db018a9acf0b40a374007ccf9aae5a1c7c85_TGliL3Rlc3QvdGVzdF90eXBpbmcucHk=..f9a067bc0dfd466e8f0c26bb3c529329e0ca49bd_TGliL3Rlc3QvdGVzdF90eXBpbmcucHk= 100644
--- a/Lib/test/test_typing.py
+++ b/Lib/test/test_typing.py
@@ -2874,7 +2874,7 @@
                          {'x': int, 'y': int})
         self.assertEqual(gth(mod_generics_cache.B),
                          {'my_inner_a1': mod_generics_cache.B.A,
-                          'my_inner_a2': mod_generics_cache.A,
+                          'my_inner_a2': mod_generics_cache.B.A,
                           'my_outer_a': mod_generics_cache.A})
 
     def test_respect_no_type_check(self):
@@ -3010,6 +3010,13 @@
             {'other': MySet[T], 'return': MySet[T]}
         )
 
+    def test_get_type_hints_classes(self):
+        class Foo:
+            y = str
+            x: y
+        # This previously raised an error under PEP 563.
+        self.assertEqual(get_type_hints(Foo), {'x': str})
+
 
 class GetUtilitiesTestCase(TestCase):
     def test_get_origin(self):
diff --git a/Lib/typing.py b/Lib/typing.py
index e606db018a9acf0b40a374007ccf9aae5a1c7c85_TGliL3R5cGluZy5weQ==..f9a067bc0dfd466e8f0c26bb3c529329e0ca49bd_TGliL3R5cGluZy5weQ== 100644
--- a/Lib/typing.py
+++ b/Lib/typing.py
@@ -1632,8 +1632,9 @@
             else:
                 base_globals = globalns
             ann = base.__dict__.get('__annotations__', {})
+            base_locals = dict(vars(base)) if localns is None else localns
             for name, value in ann.items():
                 if value is None:
                     value = type(None)
                 if isinstance(value, str):
                     value = ForwardRef(value, is_argument=False)
@@ -1635,9 +1636,9 @@
             for name, value in ann.items():
                 if value is None:
                     value = type(None)
                 if isinstance(value, str):
                     value = ForwardRef(value, is_argument=False)
-                value = _eval_type(value, base_globals, localns)
+                value = _eval_type(value, base_globals, base_locals)
                 hints[name] = value
         return hints if include_extras else {k: _strip_annotations(t) for k, t in hints.items()}
 
diff --git a/Misc/NEWS.d/next/Library/2021-01-12-23-17-02.bpo-42904.-4qkTD.rst b/Misc/NEWS.d/next/Library/2021-01-12-23-17-02.bpo-42904.-4qkTD.rst
new file mode 100644
index 0000000000000000000000000000000000000000..f9a067bc0dfd466e8f0c26bb3c529329e0ca49bd_TWlzYy9ORVdTLmQvbmV4dC9MaWJyYXJ5LzIwMjEtMDEtMTItMjMtMTctMDIuYnBvLTQyOTA0Li00cWtURC5yc3Q=
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-01-12-23-17-02.bpo-42904.-4qkTD.rst
@@ -0,0 +1,2 @@
+:func:`typing.get_type_hints` now checks the local namespace of a class when
+evaluating :pep:`563` annotations inside said class.