With the release of Firefox 22 has come an implementation of the Web Notifications (draft) API. SE Chat has had notifications for a while, but a quick search of the minified code and the lack of a notifications option indicates that it uses
window.webkitNotifications, which is of course specific to the WebKit engine.
Now, the W3C draft API is currently working on the current release versions of both Firefox and Chrome (test here) (some other browsers still only support the prefixed version for now). Would it be possible to have notification support for Firefox on SE Chat?
Previously, there was an addon that implemented
window.webkitNotifications for Firefox. Since native support was introduced, that addon has been discontinued, and no longer works on the latest version.