As of writing, the current version of Chrome (type chrome://chrome/ in the address bar to see which version you are running) supports HTTP2.
However you will need to change an internal flag to enable the H2 support as of version 40.0.2214.93 (the one my PC is running today), it is not enabled by default.
To enable H2 support, type chrome://flags/#enable-spdy4 in the address bar, click the "enable" link, and relaunch Chrome.
Once you have enabled it, it would look like this:
I would recommend installing the SPDY Indicator extension to be able to easily identify Web sites which run HTTP version 2. For example if you install this extension and visit: https://secure.akamaiflowershop.com/ you will see something like this: