In the chat faq under "How do I know when someone is talking?" section it says:
If you need to invite someone to your room, do it from the user's profile page or from the user card that pops up when you click on their avatar.
However, so far I never saw any "invite to chat" link in user profile. Wrong faq statement, or are my eyes going bad?
Also worth to mention another slight mistake - user card pops up when I hover the avatar, clicking it will take me to the profile page.