diff -uNr Python-3.7.0.orig/Lib/test/test_ssl.py Python-3.7.0/Lib/test/test_ssl.py
--- Python-3.7.0.orig/Lib/test/test_ssl.py	2018-06-26 22:07:35.000000000 -0500
+++ Python-3.7.0/Lib/test/test_ssl.py	2018-12-28 11:30:01.608382460 -0600
@@ -30,6 +30,12 @@
 PROTOCOLS = sorted(ssl._PROTOCOL_NAMES)
 HOST = support.HOST
 IS_LIBRESSL = ssl.OPENSSL_VERSION.startswith('LibreSSL')
+if IS_LIBRESSL:
+    LIBRESSL_VERSION = tuple(
+        int(s) for s in ssl.OPENSSL_VERSION.rsplit(' ')[-1].split('.')
+    )
+else:
+    LIBRESSL_VERSION = ()
 IS_OPENSSL_1_1_0 = not IS_LIBRESSL and ssl.OPENSSL_VERSION_INFO >= (1, 1, 0)
 IS_OPENSSL_1_1_1 = not IS_LIBRESSL and ssl.OPENSSL_VERSION_INFO >= (1, 1, 1)
 PY_SSL_DEFAULT_CIPHERS = sysconfig.get_config_var('PY_SSL_DEFAULT_CIPHERS')
@@ -3846,6 +3852,8 @@
                                    sni_name=hostname)
         self.assertIs(stats['client_npn_protocol'], None)
 
+    @unittest.skipIf(IS_LIBRESSL and LIBRESSL_VERSION >= (2, 6, 1),
+                     "LibreSSL 2.6.1+ has broken NPN support")
     @unittest.skipUnless(ssl.HAS_NPN, "NPN support needed for this test")
     def test_npn_protocols(self):
         server_protocols = ['http/1.1', 'spdy/2']