It depends on the chat site program, I think.
I'd make sure all internet plugins are up to date (Flash, Java, etc) and that in addition to antivirus software, you have a good firewall tool as well.
UPDATE for comment:
If the chat room operates using Java, it is running the Java program on your computer and has access to certain things that may surprise you. Most are not harmful, and part of the reasons plugins such as Java are updated so frequenly is that people are always finding new ways of getting these tools to act as security holes right into your computer.
This sounds like a simple hack, most likely using a script. Antivirus would not have caught it, generally. A firewall might have. The person was just trying to scare you and show off. They're probably not a great hacker. A skilled hacker interested in get at you would not have shown you that information but would have used what he'd learned to plant and use security holes in your system.
But then again, what do you have that a hacker is really interested in? For this reason, and this reason alone, most people will never encounter a skilled hacker attacking their own computer. Scripts and script kiddies are the ones who pull stunts and pranks like the one you experienced.