My '67 Carlton had similar specks of rust on the underside of the chain- and seat-stays. I used a wet rag and my own thumbnails to remove a lot of it, and followed with some sort of blue stuff highly recommended from the guy at my local auto parts store in Albuquerque. I was patient and this took about 4 hours.

The stays, and an old chromed Cateye bottle cage from another bike, came out quite good, and I was proud of the work I had done. But I had to attack each speck of rust independently, and this took a considerable amount of time.

The real sad story about my bike was the chrome socks on the fork. After all the rust was gone, there wasn't much chrome left. I used a reflective-silver nail polish to mask the color of the underlying steel, but the whole thing is a little too matte to be believable up close, and you can see the step height differences between the chromed areas and non-chromed areas.

Unfortunately I was laid off from my job only days after having my first long ride on it in its preliminary form. I'm still recovering a bit financially from my move to the Bay Area almost two months ago, but I do have plans of having the thing professionally refinished, chrome and all, once I can do so, but my bike looks FAR different from the condition you photographed here.