I'm not sure if you're actually supposed to be able to move chat windows in the classic Velious UI, but technically if you can resize them then you can move them as well. What I mean is this: Grab the left side of the chat window and stretch it all the way to the left of the screen. Now grab the right side of the char window and stretch it toward the left of the screen. You've effectively moved your chat window.
Barring that, you could also try
phobus or
qqui, which are both great modernized versions of the Velious UI.