Most of the advertising comes from contextual advertising once in the chat. Also with the widget that other websites use.
The advertising revenue isn't massive yet, ($4 figures/month), but it's something to build on.
There's also obviously people willing to pay for chat/communication - campfire, liveperson type services.
I'd be interested in stats on ad units and CTR (which I've always heard is really low on communication apps).
edit: Would also be interested in definition of profitability... Covering hardware/software costs? Covering costs PLUS able to eat ramen? Covering costs plus paying yourself a market salary?