I use live chat on sites that I visit quite often. I would much rather use live support than use the phone or wait around for an email. We use Customer Reach on our site and the visitors that use it seem very appreciative. You can also learn a lot about your customers and their needs during a live chat session that can help you design you products/services/site to better suit your customer's needs.

I'm not sure if I would pay another company to man the live chat simply because the person isn't completely vested in your company and customers and the quality of the support might be lower. If you could find a company that would guarantee a certain level of service and perhaps give a summary of each conversation, it might be worthwhile.