If you have moderator powers for the group you belong to, then you can kick a person from the chatroom.
If the group itself is public, then anyone can join and you can't kick.
The trick is to set it to private, then kick, and then remember to make it public again. Unfortunately once you make it public they can join again.

Originally posted by DarkCrystalMethod:

If the group itself is public, then anyone can join and you can't kick.
The trick is to set it to private, then kick, and then remember to make it public again. Unfortunately once you make it public they can join again.

Wrong.

Go to manage group members http://steamproxy-script.pipiskins.com/groups/<groupname>/membersManage and you can choose what you want to do to people. It's labelled at the top of the page with the instructions:

"Click the icon on a member to promote them to an officer or moderator
Click the icon on an officer to demote them to a member
Click the icon on a member to permanently remove them from the group"

Yeah thanks for the tips guys

If it's a public group, though (IE: Not invite only) they can simply rejoin the group.