My answer is not necessarily the best, but it is one worth checking out because of other benefits: Woopra.
Woopra is a real-time stats package; the main function is not real time chat. One of its features, however, is a real time chat client. The client can be popped open by the site visitor, similar to what you see on many ecommerce sites or - somewhat unique - forced open by the Woopra user if you spot behavior that warrants it (keep in mind the potential creepiness of that one for most sites).
If your needs run towards an analytics package other than Google, real time data, and chat, Woopra is a nice option.