After two more minutes on the chain Sunday morning, I took netviln's advice, and paid a visit to Thick. (*big shout out to cburch!*) I bought a chain tool and a chain, so I'm covered either way.
I had been using bare hands, a couple of nails as levers, and strategically aimed drops of plain old 10W40. I got it so the chain moved at all, but I could barely maintain speed on a level surface.
Note to self (and others): Winter road salt is hell on chains, especially if you don't hose them off after every ride, and oil them really really often. I was storing this bike indoors, but wasn't so good about the hosing. It irritates me that this chain is only a year old.