How can I enforce a maximum number of connections from one user with Socket.IO?

I have a very simple Socket.IO group chat system (this one). I want to prevent people from spamming new connections from their browser using JavaScript trickery. This was a problem the one time I publicized the website.

What measure should I use to prevent this? I want to count the number of connections from a browser and it it goes over a threshold, I want to drop all connections. Should I use the IP address? Is the socket.id unique to a user? How should I do it?

If you want to look at the Socket.IO code, see the highlighted code here.