I'd like to suggest that the function keys be bound to the various tabs on top of the chat window.

(F1 reserved for the Help menu accelerator key)
F2 = Game messages
F3 = Chat messages
F4 = 1st chat window
F5 = 2nd chat window
F6 = 3rd chat window
F7 = 4th chat window
F8 = 5th chat window
F9 = 6th chat window

Pressing the bound keys will switch focus of the chat window(s) to the appropriate tab.