I wouldn't use the steel wool on the chrome.
As the previous post suggests try acetone or MEK.
Also Naptha, which is a easy to get solvent. It is the main component in lighter fluid. Try soaking the spot with Ronsen or Zippo lighter fluid, hell barb-e-q fluid will do the trick. Put a piece of paper towl on it an keep it wet for about 5 minutes, Should wipe right off.