I would take it to a local bike shop. I think that's your best bet. Try to take it to a local shop that deals in higher end bikes, or somewhere like REI, not a chain sporting goods store like Dick's or Sports Authority.
The store will probably be able to fix your problem in a few minutes and may even do it for free. If not, it should only be a small fee. Also, if any parts are needed, they will probably have them on hand.
You may want to get a new chain while you're there, as the one you have is probably worn if it's as old as the bike. They'll have a tool for measuring the chain length and let you know if it needs to be replaced.
Last thing: I don't think a washer will fix your problem, but I'm not sure.