Is Chat for Multi-person chat only?

I'm thinking I'll need something a bit more robust to allow for user-to-admin only chats, as I did a test and a question asked by a third user showed up in both my (the admin) and a second user's chat window.

Is the chat plugin functionally a 'group-chat' only?

If it is, does anyone have a suggestion for a peer to peer, rather than group chat?

If it does do one-to-one chat, where is that set?