Well...you can be logged into the same campaign multiple times. Something I do is one browser window has the map/battle grid/table top (chat window is hidden), and the other browser has the chat window resized to take up most of the window. Doing something like this would allow you to rearrange your windows so Chat is on the left. Not perfect, because you'd still have to make each window active before interacting with it, but...it's close.
