"Open when YC opened"? I was under the impression we did business 24 hours a day here.
(EDIT: I now see what you mean, silly I. See below for critique, however.)
It would be possible to have it embedded in the index page, yes, but that would be rather intrusive. What's more, it would put paid to any relevancy the list of chatters had, since it would be impossible to look at the index without joining the chat.