The huge problem with chat sites is the problem of the topics being discussed in them and one of the many reasons why Google is very vague on the area and I have personally heard of sites having there adsense accounts disabled, sadly Google is pretty slack when it comes to picking and choosing which sites should not be active in their adsense scheme as legit and clean sites often do get removed from their system from no fault of their own while many sites that shouldn't have accounts carry on trading.
From what I believe and have read is that you are allowed adsense adverts on chat sites (must not be on topic of their banned topics) but your not allowed to have them within
'chat containers' and having those on the sidebar should be fine.
My advice would be to email them and provide them with the details, take screen shots of where you plan to place the advert and get an Adsense rep clarify this issue for you, least then if they do disable you at a later date they should allow release of the funds due. It's worth noting there are many other advertising companies that you can consider.
I know this answer is pretty vague but some topics on Advertising while using adsense you will find many vague areas. I know some chat sites that use Adsense, but this doesn't mean that they will not close you account as I've said they pick and choose depending which moderator reviews the account and I can only assume their own guidelines they follow are very vague and create these grey areas.