Chrome has been doing public key pinning out of the box for about three years now, though the feature has only been active for some Google properties and a couple of hand-picked high-profile sites [2]. Firefox has recently added support for static pins, plans to support the HTTP extensions exist [3].
Alternative or complementary proposals include DANE/TLSA [4] (DNS-based Authentication of Named Entities; stores certificate infos for any protocols in a new DNS record; requires DNSSEC) and TACK [5] (Trust Assertions for Certificate Keys; a similar mechanism to the one proposed in this draft but implemented as a TLS extension; possibly discontinued).
[1] https://tools.ietf.org/html/draft-ietf-websec-key-pinning-21
[2] https://www.imperialviolet.org/2011/05/04/pinning.html
[3] https://wiki.mozilla.org/SecurityEngineering/Public_Key_Pinn...
[4] https://en.wikipedia.org/wiki/DNS-based_Authentication_of_Na...
[5] http://tack.io