Zen Social Network

In this one you have a profile, and follow your friends. You can't post anything, though. On your main page, you just see who else is online.

It'd just be a white screen with avatars on them that pop in or out.

Maybe, if we go one step further, which I'm not sure about, then there could be a speech bubble you can type into. Then, it pops up a speech bubble on your avatar for a while, then goes away again, and the only people who see it are the people who were looking at you while you were there.