Why remove the chrome, you just need to give the paint something to stick to, take the finest wet/dry sandpaper you have and sand off the rust first, if you have any, second sand to the point you have a haze on the chrome then use rubber/latex gloves to keep you oily fingers off the chrome, use a paint thinner, anything that doesn't leave a residue then paint.
Wet sand between coats until you get the finish you like, this does work great, besides removing the chrome will reduce the metal on the part and increase the chance of rusting down the road.
If the paint does not stick you where not aggressive enough with the sanding or paper grit or you did not get the part clean enough. Try it you will like it and besides you can always strip the part later and then take it to the chrome shop to lighten the metal and your wallet.
Sincerly Mark, Good luck, Believe it or not.
Let me or us know how it works out.
P.S. if you use to aggressive a grit like 80 you will leave swirls that will show threw the paint.