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.
FWIW
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.
FWIW