I don't think you can and that's also something that I regret deeply, so much wasted space.
I'm not sure it would even be possible with a greasemonkey script or a browser add on.
Very nice, for some reasons vid_restart was just resizing the game not the actual window and I had to reload QL to get it working.
Too bad it doesn't seem to work well with widescreen resolution, since the Chat panel on the right doesn't move out of the way.