Let me know if you are looking out a SaaS model, I believe for chat SaaS need not be..
As this would be a web application and not with any multi tenancy or subscription mode.
In case if you are looking to build a live chat which will b for customer engagement to any site, let me know..We can have chat with asp.net, signalr, ajax technology and let me know if you are interested. Also are you expecting any live chat plugin..