diff --git a/Lib/test/test_posix.py b/Lib/test/test_posix.py
--- a/Lib/test/test_posix.py
+++ b/Lib/test/test_posix.py
@@ -16,6 +16,7 @@ import stat
 import tempfile
 import unittest
 import warnings
+import platform
 
 _DUMMY_SYMLINK = os.path.join(tempfile.gettempdir(),
                               support.TESTFN + '-dummy-symlink')
@@ -387,6 +388,9 @@ class PosixTester(unittest.TestCase):
 
     def _test_all_chown_common(self, chown_func, first_param):
         """Common code for chown, fchown and lchown tests."""
+        # test a successful chown call
+        chown_func(first_param, os.getuid(), os.getgid())
+
         if os.getuid() == 0:
             try:
                 # Many linux distros have a nfsnobody user as MAX_UID-2
@@ -398,12 +402,12 @@ class PosixTester(unittest.TestCase):
                 chown_func(first_param, ent.pw_uid, ent.pw_gid)
             except KeyError:
                 pass
-        else:
+        # HP-UX and Solaris allow a non-root user to chown to root (issue
+        # #5113)
+        elif platform.system() not in ('HP-UX', 'SunOS'):
             # non-root cannot chown to root, raises OSError
             self.assertRaises(OSError, chown_func,
                               first_param, 0, 0)
-        # test a successful chown call
-        chown_func(first_param, os.getuid(), os.getgid())
 
     @unittest.skipUnless(hasattr(posix, 'chown'), "test needs os.chown()")
     def test_chown(self):