I appreciate the replies so far.

When I look at the rear derailer from the back, it seems to be properly lined up.

Regarding the chain length, I don't know for a fact, but I believe it is the original chain. Some of the bike's parts have been changed, like the seatpost, but it had the original gum-wall tires on it when I got it, so I would think it's probable the chain is original.

Regarding the last post, from wrk101, I will research this on the 'Net, but I've never done that sort of thing before. I'm guessing it isn't rocket science, but I'm comfortable doing low-level maintenance on my cars, so I'm open to taking a shot at your suggested approach.

Would it be bad to soak the chain/freewheel in something like carburetor cleaner? I think I can get access to an auto parts cleaner or some equivalent.

Is there anything I should measure before removing the rear wheel, etc., to make sure it gets back together properly?