diff --git a/Lib/shutil.py b/Lib/shutil.py
index 2ddeb2a..98b7ea0 100644
--- a/Lib/shutil.py
+++ b/Lib/shutil.py
@@ -11,6 +11,7 @@
 import fnmatch
 from warnings import warn
 import collections
+import errno
 
 try:
     from pwd import getpwnam
@@ -105,8 +106,11 @@
     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 8d4706d..86eda39 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -287,6 +287,10 @@
 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 #7860: platform.uname now reports the correct 'machine' type
   when Python is running in WOW64 mode on 64 bit Windows.