Steel wool may scratch the chrome. Try using some tin-foil (aluminium foil) crumpled up and rub it in by hand. This will get rid of the surface rust. If the chrome is pitted then you are in trouble. I have lots of chrome on my bike - and rust mainly around the weld areas, and am planning, after cleaning, to coat the areas with 2k (2-pack) auto clear-coat which hardens quite well.
You can also get polishing discs made from cotton which you can attach to a high speed drill and use some chrome polish to get pitted areas up to a gloss finish. Keep these away from plastics as the heat of friction will melt the plastic.
Try using dry (no soap, water) Steelo, a product made from FINE steel wool.
wd-40 also works quite well, no scratches...or also toothpaste and toothbrush, rince with water.
See link below for further information.