Painting over chrome:

Start by washing with soap and water. Then clean the part with a quality wax and grease remover (PPG DX-330, DuPont Prep Sol, etc.).

If the chrome is peeling, cracking, chipping, etc., remove it by grinding (24 or 36 grit) or bring it in and have it de-chromed.

If the chrome is in decent shape (scratches are fine as long as they don't cause peeling, cracking, chipping, etc.), sand the whole part with 80 grit on a dual action sander or an angle grinder. Make sure there are no shiny spots left anywhere or it will peel.

Prime with a self-etching primer. Follow the instructions for your particular brand. They vary in application. If the self-etching primer requires sanding before top-coating, sand it according to the instructions.

If it does not require sanding, after the appropriate tack time, apply a quality primer/surfacer to fill in the 80 grit sanding marks and any other minor imperfections.

If there were any dents or dings to fill in, fill them in after applying the self-etching primer. Body filler will stick to self-etching primer, it will not stick to chrome.

If you sand through the primer at any time while sanding, you need to re-apply it to that area. Clean the part once again, using wax and grease remover (PPG DX-330) and/or final prep (PPG DX-320). I prefer DX-330 before sanding and DX-320 after sanding.

Once you are satisfied with the surface prep, you can topcoat with your favorite color and paint type.

If you are applying a spray can finish, there are some that claim to be one-step but I don't know how well they hold up after time. I have some painted-over-chrome parts out there for well over 10 years without a problem using the above methods, on cars and trucks driven on the street, not trailer queens.