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.
You will have to install a different chat system - like Skype or Google Chat. This does mean that all your friends will have to install this chat system too, which is something they might not be willing to do if you are their only friend using this system.
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 ;)