We bicycle-restoration geeks (
https://www.nonlintec.com/bikepages) run into this all the time. Usually, we need to derust something that is pretty badly corroded, in preparation for painting or getting it plated. It sounds like the problem here is a lot smaller than that--just small pitting.
Two ways to remove rust chemically: the first is with Naval Jelly, actually phosphoric acid. This takes off the rust, but leaves behind a layer of iron phosphate. That helps prevent further rusting, giving you time at least to wax or paint the cleaned surface. This protection, by itself, won't last long. It is a mess for plating, though, because the iron phosphate has to be removed. The instructions warn you against using it on chrome, but unless you have exceptionally fine chrome or leave it on a long time, you probably won't see any etching of the chrome. Also, a lot of "chrome" is really bright nickel, and it doesn't harm this either, with reasonable care.
The other way is with hydrochloric acid, which you can buy at the hardware store as muriatic acid. This should be diluted maybe 4 or 5 to 1. (Always add the acid to the water, not the water to the acid.) Just soak the part a few minutes, rinse well, wipe with a rag and the rust comes off like magic. Unfortunately, it will rerust very quickly (like, minutes), so do this only if you are going to wax, paint, or otherwise preserve the surface right away.
A few polishes will remove minor rust, too. I keep a variety of metal polishes around--they all work better or worse on various metals in various circumstances.
I never use anything abrasive on chrome. Just too much danger of scratching. Many bike-restorers swear by brass wool, but I haven't tried it.