diff --git a/Lib/test/test_logging.py b/Lib/test/test_logging.py
index bc99c3a..b884753 100644
--- a/Lib/test/test_logging.py
+++ b/Lib/test/test_logging.py
@@ -684,6 +684,7 @@
 
         self.assertEqual(len(logging._handlers), 0)
         refed_h = _OurHandler()
+        self.addCleanup(refed_h.sub_handler.stream.close)
         refed_h.name = 'because we need at least one for this test'
         self.assertGreater(len(logging._handlers), 0)
         self.assertGreater(len(logging._at_fork_reinit_lock_weakset), 1)