Having experimented with various styles when folks are messing around with the colors, I can safely tell you that -- for my eyeballs, at least -- there are no colors which truly work in all contexts.
Thoughts based on personal experience (by no means intended to be presented as Authoritative, Definitive "Evidence"), and not directly related to chatroom rules but (IMHO) just as essential to the chat "experience":
Lo these many years ago, back when I frequented a few chatrooms, I noticed that the actual chatbox and text entry box were plain, blank white. Perhaps it's personal preference, but I've always felt that to be the best option. Framing, page, etc., those could be different colors or styles, but the text boxes themselves were simple white/off-white.
Which leads me to the second half of my thoughts - the idea I keep bringing up about allowing users to choose persistent colors/fonts/styles. I found it to be VASTLY helpful in keeping up with a busy, populated chat, so I could know at a glance what was said by whom. The current system, with only one display font/style for all, gets horribly confusing to me when the chat really starts rolling. You could even experiment a little as moderator/designer and limit the choices to higher-readability fonts/styles/colors (i.e., no bright yellow!
).
A final addendum that might be linkable to the above: make chat name come directly from forum name, and link the text preferences to that account. Is this even doable? It might also have the added bonus of severely limiting the rapid-fire handle-changing if it's feasible.