Hi i am new here but not new to painting crome bumpers. I own a media blasting and restoration shop and what you need to do is have it blasted! we use aluminum oxide 120 grit to blast with it is what they use on sand paper for a grit .We use this because we can blast sheetmetal with out causing warping.But you could even sand blast the bumper it has no risk of warping.But then use a good direct to metal sealer, we use dupont variprime it is a acid type sealer works every time or ask at your paint shop for a recommendation then over that you can paint with what ever you like.GOOD LUCK JEFF
There are more than one way to do it, but if you have chips or if the chrome finish is flaking off you will need to get it totally removed by blasting or take it to a chromer to get it properly removed. If the chrome is fine and you just want to paint it you can use a product by POR-15 that can be sprayed onto the chrome to give the paint a proper surface to adhere to.