diff --git a/Lib/test/regrtest.py b/Lib/test/regrtest.py
--- a/Lib/test/regrtest.py
+++ b/Lib/test/regrtest.py
@@ -1558,17 +1558,19 @@
         except FileExistsError:
             pass
 
-    # Define a writable temp dir that will be used as cwd while running
-    # the tests. The name of the dir includes the pid to allow parallel
-    # testing (see the -j option).
-    test_cwd = 'test_python_{}'.format(os.getpid())
-    test_cwd = os.path.join(TEMPDIR, test_cwd)
+    # It is not necessary to incorporate the pid here since individual tests
+    # use support.TESTFN for parallel testing (see issue #15305).
+    test_cwd = os.path.join(TEMPDIR, 'test_python')
+    try:
+        os.mkdir(test_cwd)
+    except FileExistsError:
+        pass
 
     # Run the tests in a context manager that temporarily changes the CWD to a
-    # temporary and writable directory.  If it's not possible to create or
-    # change the CWD, the original CWD will be used.  The original CWD is
+    # temporary and writable directory.  If it's not possible to change the
+    # CWD, the original CWD is used.  In either case, the original CWD is
     # available from support.SAVEDCWD.
-    with support.temp_cwd(test_cwd, quiet=True):
+    with support.temp_cwd(path=test_cwd, quiet=True):
         main()