I had the same problem, but then I saw that I had disabled private chat globally, so maybe you should check that.

A bug when using IE still allowed me to create a private chat, if I double click the user a private chat window popped up and the invite message was sent to the user.


Also after I enabled the private chat globally it worked great in IE both via context menu and by double clicking the user. But neither context menu nor double clicking works in Firefox. The is no js error. I also made sure that Firefox allows the webpage to replace the context menu. It works great if IE user invites a Firefox user, the private chat window popps up and the users can chat together.
After looking through the code for I found out that ShowTargetUserContextMenu in CH_Skin.js.aspx is never called in Firefox.

Hope some of this helps
Ingi