Index: Lib/zipfile.py
===================================================================
--- Lib/zipfile.py	(revision 84038)
+++ Lib/zipfile.py	(working copy)
@@ -825,7 +825,9 @@
                   file=file)
 
     def testzip(self):
-        """Read all the files and check the CRC."""
+        """Read all the files and check the CRC.  Return None if all files
+        could be read successfully, or the name of the offending file
+        otherwise."""
         chunk_size = 2 ** 20
         for zinfo in self.filelist:
             try:
Index: Lib/test/test_zipfile64.py
===================================================================
--- Lib/test/test_zipfile64.py	(revision 84038)
+++ Lib/test/test_zipfile64.py	(working copy)
@@ -60,6 +60,7 @@
                    '  zipTest still writing %d of %d, be patient...' %
                    (num, filecount)), file=sys.__stdout__)
                 sys.__stdout__.flush()
+        
         zipfp.close()
 
         # Read the ZIP archive
@@ -73,6 +74,10 @@
                    '  zipTest still reading %d of %d, be patient...' %
                    (num, filecount)), file=sys.__stdout__)
                 sys.__stdout__.flush()
+
+        # Check that testzip thinks the archive is valid
+        self.assertIsNone(zipfp.testzip())
+
         zipfp.close()
 
     def testStored(self):
@@ -113,6 +118,25 @@
             self.assertEqual(content, "%d" % (i**3 % 57))
         zipf.close()
 
+    def testziptest(self):
+        # check that testzip can be used on archives containing very
+        # large files (about 1GB)
+        datablock = ''.join([chr(x) for x in range(1,256)])
+        datablock *= 4096
+        f = open(TESTFN2,'w')
+        for i in range(1024):
+            f.write(datablock)
+        f.close()
+
+        zipf = zipfile.ZipFile(TESTFN, "w", zipfile.ZIP_DEFLATED, 
+                               allowZip64=True)
+        zipf.write(TESTFN2)
+        zipf.close()
+
+        zipf2 = zipfile.ZipFile(TESTFN, mode="r")
+        self.assertIsNone(zipf2.testzip())
+        zipf.close()
+
     def tearDown(self):
         support.unlink(TESTFN)
         support.unlink(TESTFN2)
Index: Lib/test/test_zipfile.py
===================================================================
--- Lib/test/test_zipfile.py	(revision 84038)
+++ Lib/test/test_zipfile.py	(working copy)
@@ -97,8 +97,9 @@
                 self.assertEqual(info.filename, nm)
                 self.assertEqual(info.file_size, len(self.data))
 
-            # Check that testzip doesn't raise an exception
-            zipfp.testzip()
+            # Check that testzip thinks the archive is ok
+            # (it returns None if all contents could be read properly)
+            self.assertIsNone(zipfp.testzip())
 
     def test_stored(self):
         for f in (TESTFN2, TemporaryFile(), io.BytesIO()):