Game lobby?

Question

I want to make a sort of game lobby for a chess game. After two computers have a connection with eachother I guess it wouldn't be much harder than just sending a string from one computer to another but the problem lies in showing who wants to play and getting the IP address of that person (I can't possible expect from the user to know the other person's IP, that wouldn't be very user-friendly).

Personally I thought of having the names and IP's of the potential players on the Internet. When the user wants to play a game against someone, the program just adds the name and IP of the user, reads the rest of the names and shows them. When the suer has selected a person to play with a request for a game is then send etc...

I thought that a database placed online would do this (which should be free, easy access to it with a program and doesn't require my computer to be on all the time) but so far I had no success...

Or maybe there's another way? How do other games have multiplayer? (note: I'm not going buy anything (soft- or hardware))