diff --git a/Lib/shutil.py b/Lib/shutil.py
index 892a94cc41a..9625d362330 100644
--- a/Lib/shutil.py
+++ b/Lib/shutil.py
@@ -160,8 +160,10 @@ def copystat(src, dst, symlinks=False):
         try:
             chflags_func(dst, st.st_flags)
         except OSError as why:
-            if (not hasattr(errno, 'EOPNOTSUPP') or
-                why.errno != errno.EOPNOTSUPP):
+            for err in 'EOPNOTSUPP', 'ENOTSUP':
+                if hasattr(errno, err) and why.errno == getattr(errno, err):
+                    break
+            else:
                 raise
 
 def copy(src, dst, symlinks=False):
diff --git a/Lib/test/test_shutil.py b/Lib/test/test_shutil.py
index 6c9515e409f..4700a49b003 100644
--- a/Lib/test/test_shutil.py
+++ b/Lib/test/test_shutil.py
@@ -282,6 +282,35 @@ class TestShutil(unittest.TestCase):
         self.assertTrue(abs(os.stat(src).st_mtime - os.stat(dst).st_mtime) <
                         00000.1)
 
+    @unittest.skipUnless(hasattr(os, 'chflags') and
+                         hasattr(errno, 'EOPNOTSUPP') and
+                         hasattr(errno, 'ENOTSUP'),
+                         "requires os.chflags, EOPNOTSUPP & ENOTSUP")
+    def test_copystat_handles_harmless_chflags_errors(self):
+        tmpdir = self.mkdtemp()
+        file1 = os.path.join(tmpdir, 'file1')
+        file2 = os.path.join(tmpdir, 'file2')
+        write_file(file1, 'xxx')
+        write_file(file2, 'xxx')
+
+        def make_chflags_raiser(err):
+            ex = OSError()
+
+            def _chflags_raiser(path, flags):
+                ex.errno = err
+                raise ex
+            return _chflags_raiser
+        old_chflags = os.chflags
+        try:
+            for err in errno.EOPNOTSUPP, errno.ENOTSUP:
+                os.chflags = make_chflags_raiser(err)
+                shutil.copystat(file1, file2)
+            # assert others errors break it
+            os.chflags = make_chflags_raiser(errno.EOPNOTSUPP + errno.ENOTSUP)
+            self.assertRaises(OSError, shutil.copystat, file1, file2)
+        finally:
+            os.chflags = old_chflags
+
     @support.skip_unless_symlink
     def test_copy_symlinks(self):
         tmp_dir = self.mkdtemp()
diff --git a/Misc/NEWS b/Misc/NEWS
index 6ef515449de..2f11eefd58a 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -23,6 +23,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #14662: Prevent shutil failures on OS X when destination does not
+  support chflag operations.  Patch by Hynek Schlawack.
+
 - Issue #14157: Fix time.strptime failing without a year on February 29th.
   Patch by Hynek Schlawack.