Google has a plugin for Chrome called End to End which will allow exactly that. However, it's currently in alpha, and has to be compiled yourself. There's no word on if it will ever be an official part of chrome.
It supports Elliptic Curve Cryptography as part of OpenPGP (RFC 4880RFC 4880 — OpenPGP Message Format, and RFC 6637RFC 6637 — Elliptic Curve Cryptography (ECC) in OpenPGP ), and operates in JavaScript inside of Chrome, utilizing local storage for key storage. The key database is encrypted when Chrome is not running, and sandboxed when Chrome is running, so it should be relatively secure.