Can be done, however the prep work is crucial to make sure the paint stays attached to the chrome plating.
You'll need to scuff the chrome up so there is NO shine left, 320 grit should do it but 240 works well on orbital/machine sanding etc.
Use a good hi build primer, guide coat and rub back with 320.
Then paint with your preffered gloss black, I'd go 2k unless you want a metallic in it as then there's no clear coat to worry about with brake dust etc.