It apparently used to be the case that the robots.txt file on chat.stackexchange.com allowed search engines to index some parts of that domain; this robots.txt file was apparently intended to allow crawling of chat transcripts, though that question suggests it didn't actually work.
Now, however, it is set to disallow crawling of the entire domain, explicitly preventing chat transcripts from being indexed.
However, this does not work; a Google search for site:chat.stackexchange.com transcripts shows that chat transcripts in fact are being indexed thoroughly. I think that the intended behavior--telling crawlers not to index chat transcripts--is marginally preferable from a privacy perspective (not, of course, that SE chat is really intended to be private).
I believe that the reason for this not working is fairly simple; although that robots.txt file is valid, it is returned with HTTP status code 418 ("I'm a Teapot") rather than 200. Crawlers generally ignore robots.txt files returned with error status codes and I believe that this is why Google is not respecting that robots.txt file.
I suggest fixing this by changing the status code to a 200, either keeping the current policy (disallowing indexing) in place or committing to allowing the indexing of chat transcripts. I'd prefer the former but regardless the current behavior is a bug.