I really like Ubuntu, but one minor annoyance I've always had with it is that, when using a web browser that places its tabs at the top of the application (Chrome in my case, though Firefox does this too), the unity panel (bar at the top of the screen) prevents the browser tabs from being placed at the very top of the screen. This makes it marginally more difficult for me to position my mouse over the tabs, as I have to worry about my mouse's vertical positioning instead of just pushing it all the way to the top of the screen as I do on Windows.

Is there a way to hide this annoying bar or move it to the bottom of the screen so my browser tabs can utilize that valuable piece of screen real-estate instead of it being wasted on menu items I rarely use? (Or alternately, a solution like this would also be acceptable.)