Use "The Every Day Chat Room" to talk to anyone and the "Gold Star Chats" to talk to other Premium members.
"Private Chat" is a room we use for meetings - the Big GTG organizers are using it. I will change the description of that chat room so that is more clear.
You can't have a chat that is completely private. Even in the Gold Star Chat Room, someone can join in, but you see their name in the list. For a completely private exchange, use private messages.