Great idea, but I can see few practical problems:

1) It has the same catch-22 problem like dating. Unless there are many users already chatting on the site Im visiting, theres no point for me to install this plugin.It maybe better if you target some small segment of people with similar browsing interests, like people who spend a lot of time in social networks, youtube etc.

2)http://www.visitrs.com/ doesnt have any content other than a login screen and the screenshots on mozilla.org is minimal. Some more screenshots would help.

3) What will I chat with strangers on a site? or will I even see a list of users currently willing to chat? Will I see the stream of messages between other "chatters" like chat rooms?