For a paint to properly bond to a chromed surface, the surface needs to be prepped (sanded, scuffed, blasted, etc.) to a water break free condition, and then cleaned with an alcohol solvent to be free of contaminants. any contaminants will create a weak bond, and may cause flaking after many cycles of cold to hot to cold, etc.
below is an article, for a different hobby of mine, but it describes obtaining a water break free surface to get a good surface bond and prevent any flaking or cracking. Easily applied to painting over chrome.
For chrome, use heavy steel wool or sand blasting, as stated above, to knock down the surface sheen.
http://www.rodbuilding.org/library/waterfree.html