I was so happy to find a work around for this. A couple of months ago I invited a friend who already uses a Gmail to chat. He never got the invite. He invited me, and I never got his either. We can chat via AIM, so it was not a big deal. Yesterday I finally looked up the issue on Google Group and was very happy to find an answer that worked for me.
Unfortunately, I cannot find the exact forum topic link again, but if you have this issue try going to the secure version of Gmail at https://mail.google.com and then have your friend resend the invite.
No clue why this works, but it worked for me!