Huh. I poked around in both the general chat room and in one-on-one chat. All I could find was a way to clear the current screen, not to completely delete a chat thread. It makes sense, though: if there's abuse going on, the moderators / owners of the site should be able to see it. However, it's possible that we both missed something. I posted a link to this thread in Site Announcements and Information just in case there's more to it.