This is using part of a chatroom where other people can't see what you're saying.
Never agree to a private chat with someone unless you already know them face-to-face, in real life.
You can also have private chats on "instant messaging".
Instant messaging - sometimes shortened to IM - is a computer program that allows you to send messages that other users receive straight away.
It is best only to do this with people you already know in real life.
If you get to a chatroom through instant messaging, remember to follow the same safety rules you would use if you were chatting anywhere else.