Adam,
I'm not really sure why it's doing this, but it seems like I was able to help the problem a little by making the overflow property of #chat_layout_message style "scroll" instead of "auto" (in the /CuteChat/CH_style.css file). Now it doesn't seem expand the page out of view until someone types in a word that has to wrap to the next line. Could it be one of the word wrap CSS properties causing this conflict with Firefox?