diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 38fdf3f..66369fe 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -4428,6 +4428,37 @@
                 s.write(b'PHA')
                 self.assertIn(b'WRONG_SSL_VERSION', s.recv(1024))
 
+    def test_bpo37428_pha_cert_none(self):
+        # verify that post_handshake_auth does not implicitly enable cert
+        # validation.
+        hostname = SIGNED_CERTFILE_HOSTNAME
+        client_context = ssl.SSLContext(ssl.PROTOCOL_TLS_CLIENT)
+        client_context.post_handshake_auth = True
+        client_context.load_cert_chain(SIGNED_CERTFILE)
+        # no cert validation and CA on client side
+        client_context.check_hostname = False
+        client_context.verify_mode = ssl.CERT_NONE
+
+        server_context = ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER)
+        server_context.load_cert_chain(SIGNED_CERTFILE)
+        server_context.load_verify_locations(SIGNING_CA)
+        server_context.post_handshake_auth = True
+        server_context.verify_mode = ssl.CERT_REQUIRED
+
+        server = ThreadedEchoServer(context=server_context, chatty=False)
+        with server:
+            with client_context.wrap_socket(socket.socket(),
+                                            server_hostname=hostname) as s:
+                s.connect((HOST, server.port))
+                s.write(b'HASCERT')
+                self.assertEqual(s.recv(1024), b'FALSE\n')
+                s.write(b'PHA')
+                self.assertEqual(s.recv(1024), b'OK\n')
+                s.write(b'HASCERT')
+                self.assertEqual(s.recv(1024), b'TRUE\n')
+                # server cert has not been validated
+                self.assertEqual(s.getpeercert(), {})
+
 
 HAS_KEYLOG = hasattr(ssl.SSLContext, 'keylog_filename')
 requires_keylog = unittest.skipUnless(
diff --git a/Misc/NEWS.d/next/Library/2019-06-27-13-27-02.bpo-37428._wcwUd.rst b/Misc/NEWS.d/next/Library/2019-06-27-13-27-02.bpo-37428._wcwUd.rst
new file mode 100644
index 0000000..2cdce6b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-06-27-13-27-02.bpo-37428._wcwUd.rst
@@ -0,0 +1,4 @@
+SSLContext.post_handshake_auth = True no longer sets
+SSL_VERIFY_POST_HANDSHAKE verify flag for client connections. Although the
+option is documented as ignored for clients, OpenSSL implicitly enables cert
+chain validation when the flag is set.
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index 2331c58..3351af6 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -963,6 +963,26 @@
     SSL_set_mode(self->ssl,
                  SSL_MODE_ACCEPT_MOVING_WRITE_BUFFER | SSL_MODE_AUTO_RETRY);
 
+#ifdef TLS1_3_VERSION
+    if (sslctx->post_handshake_auth == 1) {
+        if (socket_type == PY_SSL_SERVER) {
+            /* bpo-37428: OpenSSL does not ignore SSL_VERIFY_POST_HANDSHAKE.
+             * Set SSL_VERIFY_POST_HANDSHAKE flag only for server sockets and
+             * only in combination with SSL_VERIFY_PEER flag. */
+            int mode = SSL_get_verify_mode(self->ssl);
+            if (mode & SSL_VERIFY_PEER) {
+                int (*verify_cb)(int, X509_STORE_CTX *) = NULL;
+                verify_cb = SSL_get_verify_callback(self->ssl);
+                mode |= SSL_VERIFY_POST_HANDSHAKE;
+                SSL_set_verify(self->ssl, mode, verify_cb);
+            }
+        } else {
+            /* client socket */
+            SSL_set_post_handshake_auth(self->ssl, 1);
+        }
+    }
+#endif
+
     if (server_hostname != NULL) {
         if (_ssl_configure_hostname(self, server_hostname) < 0) {
             Py_DECREF(self);
@@ -2986,10 +3006,10 @@
                         "invalid value for verify_mode");
         return -1;
     }
-#ifdef TLS1_3_VERSION
-    if (self->post_handshake_auth)
-        mode |= SSL_VERIFY_POST_HANDSHAKE;
-#endif
+
+    /* bpo-37428: newPySSLSocket() sets SSL_VERIFY_POST_HANDSHAKE flag for
+     * server sockets and SSL_set_post_handshake_auth() for client. */
+
     /* keep current verify cb */
     verify_cb = SSL_CTX_get_verify_callback(self->ctx);
     SSL_CTX_set_verify(self->ctx, mode, verify_cb);
@@ -3735,8 +3755,6 @@
 #if TLS1_3_VERSION
 static int
 set_post_handshake_auth(PySSLContext *self, PyObject *arg, void *c) {
-    int (*verify_cb)(int, X509_STORE_CTX *) = NULL;
-    int mode = SSL_CTX_get_verify_mode(self->ctx);
     if (arg == NULL) {
         PyErr_SetString(PyExc_AttributeError, "cannot delete attribute");
         return -1;
@@ -3748,17 +3766,8 @@
     }
     self->post_handshake_auth = pha;
 
-    /* client-side socket setting, ignored by server-side */
-    SSL_CTX_set_post_handshake_auth(self->ctx, pha);
-
-    /* server-side socket setting, ignored by client-side */
-    verify_cb = SSL_CTX_get_verify_callback(self->ctx);
-    if (pha) {
-        mode |= SSL_VERIFY_POST_HANDSHAKE;
-    } else {
-        mode ^= SSL_VERIFY_POST_HANDSHAKE;
-    }
-    SSL_CTX_set_verify(self->ctx, mode, verify_cb);
+    /* bpo-37428: newPySSLSocket() sets SSL_VERIFY_POST_HANDSHAKE flag for
+     * server sockets and SSL_set_post_handshake_auth() for client. */
 
     return 0;
 }