diff --git a/OpenSSL/SSL.py b/OpenSSL/SSL.py
index fbb18f0..40fe5a6 100644
--- a/OpenSSL/SSL.py
+++ b/OpenSSL/SSL.py
@@ -161,7 +161,7 @@
 
 
 class _VerifyHelper(object):
-    def __init__(self, connection, callback):
+    def __init__(self, callback):
         self._problems = []
 
         @wraps(callback)
@@ -171,6 +171,10 @@
             error_number = _lib.X509_STORE_CTX_get_error(store_ctx)
             error_depth = _lib.X509_STORE_CTX_get_error_depth(store_ctx)
 
+            index = _lib.SSL_get_ex_data_X509_STORE_CTX_idx()
+            ssl = _lib.X509_STORE_CTX_get_ex_data(store_ctx, index)
+            connection = Connection._reverse_mapping[ssl]
+
             try:
                 result = callback(connection, cert, error_number, error_depth, ok)
             except Exception as e:
@@ -542,7 +546,7 @@
         if not callable(callback):
             raise TypeError("callback must be callable")
 
-        self._verify_helper = _VerifyHelper(self, callback)
+        self._verify_helper = _VerifyHelper(callback)
         self._verify_callback = self._verify_helper.callback
         _lib.SSL_CTX_set_verify(self._context, mode, self._verify_callback)
 
diff --git a/OpenSSL/test/test_ssl.py b/OpenSSL/test/test_ssl.py
index bfe3114..369b1b6 100644
--- a/OpenSSL/test/test_ssl.py
+++ b/OpenSSL/test/test_ssl.py
@@ -277,6 +277,19 @@
                         write.bio_write(dirty)
 
 
+    def _handshakeInMemory(self, client_conn, server_conn):
+        client_conn.set_connect_state()
+        server_conn.set_accept_state()
+
+        for conn in [client_conn, server_conn]:
+            try:
+                conn.do_handshake()
+            except WantReadError:
+                pass
+
+        self._interactInMemory(client_conn, server_conn)
+
+
 
 class VersionTests(TestCase):
     """
@@ -981,6 +994,34 @@
                     pass
 
 
+    def test_set_verify_callback_connection_argument(self):
+        """
+        The first argument passed to the verify callback is the
+        :py:class:`Connection` instance for which verification is taking place.
+        """
+        serverContext = Context(TLSv1_METHOD)
+        serverContext.use_privatekey(
+            load_privatekey(FILETYPE_PEM, cleartextPrivateKeyPEM))
+        serverContext.use_certificate(
+            load_certificate(FILETYPE_PEM, cleartextCertificatePEM))
+        serverConnection = Connection(serverContext, None)
+
+        class VerifyCallback(object):
+            def callback(self, connection, *args):
+                self.connection = connection
+                return 1
+
+        verify = VerifyCallback()
+        clientContext = Context(TLSv1_METHOD)
+        clientContext.set_verify(VERIFY_PEER, verify.callback)
+        clientConnection = Connection(clientContext, None)
+        clientConnection.set_connect_state()
+
+        self._handshakeInMemory(clientConnection, serverConnection)
+
+        self.assertIdentical(verify.connection, clientConnection)
+
+
     def test_set_verify_callback_exception(self):
         """
         If the verify callback passed to :py:obj:`Context.set_verify` raises an