I had a Facebook account, and deleted it, since I found Facebook overwhelming. Now, I would just like to chat (using web app or computer program) with some of my Facebook friends, so I wonder if this is possible, without creating a new Facebook account or trying to recover my old one.
There is actually a way, although like Dez said in a comment, you will still need an active Facebook account.
If you download a chat client like Pidgin, you can log in to facebook chat from there, using your account. You will never have to log in to the actual site, or even update it with posts, and all your facebook friends will see you online.
You will simply be chatting to them using your chat client ;)