Mastodon doesn't have chat rooms, but our matrix instance does! Just like Mastodon, Matrix allows you to communicate with other people across various networks (telegram, irc, discord, etc) and across various servers via bots and federation. There's a whole world out there!
You can use our web client at
https://element.rainbo.ws
and/or
download the Element app on your mobile device: enter https://matrix.rainbo.ws as your "custom homeserver" and click "sign up"