I think you can try 123 live help, it is a family product for 123 Flash Chat Software;
It supports video chat, and all the chat logs will be kepted both on server and operator panel.
Also, it supports user invitation function to get more users to be interactive. And you can check all the visitors' info to help you to do SEO, how many users are currently on your page, from which referal links, and their landing pages etc.
It is a perfect live video chat script.