diff --git a/Lib/shutil.py b/Lib/shutil.py
index dc36820dc9a..78504b9d3fb 100644
--- a/Lib/shutil.py
+++ b/Lib/shutil.py
@@ -9,6 +9,7 @@ import sys
 import stat
 from os.path import abspath
 import fnmatch
+import errno
 
 __all__ = ["copyfileobj","copyfile","copymode","copystat","copy","copy2",
            "copytree","move","rmtree","Error", "SpecialFileError"]
@@ -88,8 +89,11 @@ def copystat(src, dst):
     if hasattr(os, 'chmod'):
         os.chmod(dst, mode)
     if hasattr(os, 'chflags') and hasattr(st, 'st_flags'):
-        os.chflags(dst, st.st_flags)
-
+        try:
+            os.chflags(dst, st.st_flags)
+        except OSError as why:
+            if not hasattr(errno, 'EOPNOTSUPP') or why.errno != errno.EOPNOTSUPP:
+                raise
 
 def copy(src, dst):
     """Copy data and mode bits ("cp src dst").
diff --git a/Misc/NEWS b/Misc/NEWS
index 1c329dd2662..f82919b43fd 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -17,6 +17,10 @@ Core and Builtins
 Library
 -------
 
+- Issue #7512: shutil.copystat() could raise an OSError when the filesystem
+  didn't support chflags() (for example ZFS under FreeBSD).  The error is
+  now silenced.
+
 - Issue #3890: Fix recv() and recv_into() on non-blocking SSL sockets.
 
 - Issue #6716/2: Backslash-replace error output in compilall.