Index: Python/ceval.c
===================================================================
--- Python/ceval.c	(revision 66053)
+++ Python/ceval.c	(working copy)
@@ -2095,7 +2095,16 @@
 		case FOR_ITER:
 			/* before: [iter]; after: [iter, iter()] *or* [] */
 			v = TOP();
-			x = (*v->ob_type->tp_iternext)(v);
+			if (v->ob_type->tp_iternext != NULL)
+				x = (*v->ob_type->tp_iternext)(v);
+			else {
+				PyErr_Format(PyExc_TypeError,
+					"%.200s is no longer an iterator",
+					v->ob_type->tp_name);
+				err = -1;
+				break;
+			}
+
 			if (x != NULL) {
 				PUSH(x);
 				PREDICT(STORE_FAST);
Index: Lib/test/test_iter.py
===================================================================
--- Lib/test/test_iter.py	(revision 66053)
+++ Lib/test/test_iter.py	(working copy)
@@ -853,7 +853,22 @@
         self.assertEqual(list(b), list(zip(range(5), range(5))))
         self.assertEqual(list(b), [])
 
+    def test_3720(self):
+        # Avoid a crash, when an iterator deletes its __next__() method.
+        class BadIterator(object):
+            def __iter__(self):
+                return self
+            def __next__(self):
+                del BadIterator.__next__
+                return 1
 
+        try:
+            for i in BadIterator() :
+                pass
+        except TypeError:
+            pass
+
+
 def test_main():
     run_unittest(TestCase)