Turtle Wax Chrome polilsh is amzing stuff, try it. If they are too far gone all you have to do is sand them to scuff up the surface, clean real good with metal prep or some other solution that will remove all the dirt grease and wax. Spray a coat of red oxide primer and then whatever colour you want.
Check around your area and see if someone does powder coating. It's more durable and will definitely bake onto chrome. Otherwise you've got a heavy job to scuff the chrome well enough to accept and let the primer or paint bind to it. If you don't scuff it well, down the road the paint will blister and peel / chip off.
Well on my 280zx i converted my window trim from chrome to black. Looks great. I sanded the chrome off, started with a 100 grit, then went to a 180 grit, then finished with a 240 grit. Then I primed it, Pained it with a rust paint (2 coats), then took enamel paint (2 coats), the finished up with 2 coats of clear coat. Worked great, now for the test of time. But in you situation its bumper chrome so it may be harder to get off and down the the bar metal like I did. Hope this helps.