The Chromium team has implemented http2 and provided support for it in the dev and beta channel for a long time. Starting with Chrome 40, released on January 27th 2015, http2 is enabled by default for a certain amount of users. The amount started off really small and then increased gradually over time.
SPDY support was removed in Chrome 51 in favor of http2. In a blog post, the project announced in February 2016:
“Over 25% of resources in Chrome are currently served over HTTP/2, compared to less than 5% over SPDY. Based on such strong adoption, starting on May 15th — the anniversary of the HTTP/2 RFC — Chrome will no longer support SPDY.”
If you use a very old Chrome version you may want to check if the support is there.
Enter “chrome://flags/#enable-spdy4" in your browser's address bar and click “enable” if it isn't already showing it as enabled. This flag has been removed in recent version and the support is now always implied.
Remember that Chrome only implements http2 over TLS. You will only ever see http2 in action with Chrome when going to https:// sites that offer http2 support.
There are Chrome plugins available that helps visualize if a site is using HTTP/2. One of them is “HTTP/2 and SPDY Indicator”.
Chrome's current experiments with QUIC (see section 12.1) dilute the HTTP/2 numbers somewhat.