diff --git a/Lib/test/test_capi.py b/Lib/test/test_capi.py
index 78c51b3cb61..2761ab3f209 100644
--- a/Lib/test/test_capi.py
+++ b/Lib/test/test_capi.py
@@ -350,9 +350,11 @@ class CAPITest(unittest.TestCase):
         for i in range(1000):
             L = MyList((L,))
 
+    @support.requires_resource('cpu')
     def test_trashcan_python_class1(self):
         self.do_test_trashcan_python_class(list)
 
+    @support.requires_resource('cpu')
     def test_trashcan_python_class2(self):
         from _testcapi import MyList
         self.do_test_trashcan_python_class(MyList)
diff --git a/Misc/NEWS.d/next/Tests/2019-11-21-09-11-06.bpo-38875.wSZJal.rst b/Misc/NEWS.d/next/Tests/2019-11-21-09-11-06.bpo-38875.wSZJal.rst
new file mode 100644
index 00000000000..3f6c86d3226
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-11-21-09-11-06.bpo-38875.wSZJal.rst
@@ -0,0 +1 @@
+test_capi: trashcan tests now require the test "cpu" resource.