It appears there is some trouble with logged in users and the chat site. I noticed this while trying to access the Android SE chatroom, but wound up having the same error over and over:
POST http://chat.stackexchange.com/users/login/global 404 (Not Found)
I tried hiding the notification and clicking the "log in" link, but the page just refreshed with the same 404 error. The only difference is that the return URL gets increasingly confusing, and after a few clicks I ended up with
Next, I came over to meta.stackoverflow.com to write this and I noticed in the Console I had forgotten to close:
POST http://meta.stackoverflow.com/users/login/global 404 (Not Found), on every page until I logged in again from the
log in link on this site, which worked. The weird part is, every other site I already was logged into still worked normally.
I suspect that this is not restricted to this specific chat, hence the [all-sites] tag