This might be a little late, but I just stumbled across a TiddlyWiki[1] that has a nicely-working shoutbox from Shoutbox.us[2].
It seems to be quite easy to install with any website (it's just an IFRAME). So it should be rather simple to integrate this into MW as well (e.g. by adding the necessary IFRAME to MediaWiki:Sidebar) - without the need for an extension.
However, I myself can't use this one, as it's hosted by Shoutbox.us themselves - and running conversations through some random company's server would most likely create confidentiality issues in a corporate environment... Nevertheless, maybe someone else can benefit from it.
-- F.