Getting paint to stick to Chrome is tough. About the only types of paint that I've encountered that will actually stick are the two part epoxy, and the baked on powder coats.
About the only thing I would suggest is that you scuff the chrome as much as possible, then making sure you have cleaned the article real well, apply either epoxy primer or Zinc Oxide primer, then top coat per primer instructions. (i.e. topcoat within x hours and no sanding required, or scuff and paint)
By the way, when you scuff the chrome, you're not looking to polish it, you're looking to leave some scratches for the primer to adhere to.
Get yourself some "BULLDOG" Adhesion Promotor. This product makes paint stick to all automotive surfaces. Works on chrome, plastic, vinyl, even on fiberglass to galvanized metal and glass.
Follow the direction and it'll work great for you
I used this spray bomb of trim paint, matt black. It has'nt peeled yet, and has been on there for three months. I scuffed it with 400 grit til it did'nt shine and carefully masked it all off, wiped it with laquer thiner and sprayed away, no primer. I like the black alot better than the chrome.