Bugs are evil nasty critters that get into the site and break it; Help us exterminate!
We've reported this to the chat people, but given that clearing the cache does solve the problem, it certainly seems to be a browser problem.
The problem does not occur with Opera or Firefox...
... And started happening without any updates having been done to chat.
Also, it started for most people a few days ago to a couple weeks ago and seems that it may have happened in conjunction with an auto-update to either IE 7 or windows XP. I'm pretty sure I don't have this problem on my computers running Vista, just XP... which may indicate it was an "Explorer" update that caused the problem, rather than internet explorer itself.