It is already displaying the groups you're a part of - if you want to confirm this, log out and try this link:
http://www.chess.com/members/view/rhoskins
I can see you're a member of
Chess Athenians
12 members
History Discussion
2 members
Northeast Ohio
5 members
The Meeting Place
13 members
TT Perry
3 members
How do I change the content on the sidebar of my public profile?
e.g. How do I add the groups I belong to.