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Comments and chat serve two very different purposes.  Comments should only be for communicating with the author about modifications to the post.  These should not be conversations or chit-chat.  In a lot of situations, allowing such chit-chat would seriously degrade what people come to the site for.

Chat, on the other hand, is for side conversations and intended to include back and forth, perhaps between multiple users.  That has it's place, but I would certainly NOT want to see it on a Q&A page.  Let's keep those clean.  

Chat is very messy and noisy by its nature.  That's fine when you go to a particular page just for that.  But, that place should not be a Q&A page.

In all the years I was on SE, I looked at chat maybe a dozen times at most. Each time I remember thinking <i>"Yuk, what a mess"</i> and got out of there fast.  I realize some people are into that, but there are also plenty of people like me who are here because it's NOT a kaffeeklatsch.

The solution is to keep Q&A and chat solidly separated.  Off to the side is not separate enough, not to mention visually cluttered regardless of what's over there.