If you need a private internet chatroom (Facebook Chat and Lync IM are NOT private), you need to check out Hack Chat. It is dirt simple to use and totally free. Just concoct a chatroom name and distribute the corresponding URL.
For example, let’s say you choose a chatroom called lk8a–afe. You simply alert your chat buddies to go to https://hack.chat.com/?lk8a–afe.
It’s that simple. No record of the chatroom’s existence is saved by Hack Chat, neither is any message history.
If you’re REALLY concerned with privacy
Of course records of the chatroom’s existence will be recorded forever by your email provider, or however you choose to broadcast it. Just choose a chatroom name that’s sufficiently random and change it up every so often. Perform those chat’s behind a VPN and avoid personal details in the chat if you are really concerned.