Set the project property full screen to on (possibly scale mode) and press F11. Your browser should "disappear".
It works in FF and Chrome.
Normally some actions from the browser plugin should allow it too.
Nevertheless as you can try in this capx it doesn't seem to work in Firefox, and works half in chrome (In chrome once in fullscreen, I don't see the button anymore and clicking the sprite doesn't seem to cancel the fullscreen).
@Ashley should I file a bug report or did I screwed the capx ?