Depends on how deep the scratches/swirls are and how thick the plating is. Might want to try #0000 steel wool and some chrome polish from Mothers or Meguiars. Hand polishing could take a good while, 15-20 minutes of work on a small area.
If you can remove the part and polishing it on a wheel, there are numerous chrome polishing kits available from places like Eastwood.com and others. A quick internet search will turn up info for you.
Personally, I've never had much luck polishing out scratches from chrome, but I don't have a lot of patience for the process. If you do, you might be able to make it work.