Google Chrome will no longer support HTTP/2 on vanilla 14.04 after May 15th [0], even if you're using the latest official upstream NGINX packages. This is because 14.04 ships with a version of OpenSSL that does not support the ALPN extension (prior to OpenSSL 1.0.2 you're limited to NPN, now deprecated). There was a bit of back-and-forth about the exact date, as the change was originally scheduled for earlier. However, Chrome decided to specifically push back the date so that there would be an Ubuntu LTS release available with the required support [1]. If you're still stuck on SPDY, that's going to be dropped too, so there's really no good reason not to simply use HTTP/2 at this point.
[0] http://blog.chromium.org/2016/02/transitioning-from-spdy-to-...
[1] https://bugs.chromium.org/p/chromium/issues/detail?id=557197