Some folks here hang around in the chat room pretty well like Snailboat, Cerbeus and myself. So I guess it becomes problematic for any of us to know when a new question is posted to the site. I saw such a feature in Movies.SE chat room where a bot Movie-Reel displays the question in the chat room as soon as a new question is posted. I suggest creating a similar bot here who would carry out the same function here. This feature will help people like us to keep track of new questions, if posted. So I request the SE employees and mods here to think about implementing it.
This can be done by any room owner. The ELL chat room currently doesn't have any explicit owners, but any moderator is implicitly an owner and as such can a) add feeds, and b) appoint other users as explicit room owners.
There's a way to do this, as balpha pointed out (I'm not exactly sure of each step in the process, but I think I could figure it out). So if this is something the community wants, it shouldn't be hard to do.
I don't know that it's a very good idea though. I forget exactly who I was talking to, but some time ago I was talking to moderators of other sites, and they said that the question feed killed their chat room. They said that whenever a question popped up it killed the flow of discussion, because the ratio of questions to messages wasn't low enough. We get a decent amount of questions, and so I think this has a good chance of happening to us. The Teacher's Lounge has a feed thingy that posts any MSO questions re: moderator-tools and that doesn't kill discussion, but that's not every question being posted, just a special subset.
So, doing this is relatively easy. Whether or not we should is another question. (Alternately there's the cool little popup thingy that shows up in the ELU room that goes away after a minute; maybe we should find out how they do that?) If the community wants to go forward with either of these options I'd be happy to investigate.