Just reading your post, I do remember seeing those chrome grills back in the day.
Iv been a auto painter for 30+ years and use to be sceptical in painting chrome and wether it would stick to it.
Have painted several chrome parts now with no come backs, not saying that this is the only way. But has been working for me.
I would sand with 220-180 grit thoroughly, for a mechanical scratch. Now this is the key, we get Acid wipes for prep on bare metal including chrome. They fairly easy to use, just be thorough wiping and make sure all area's are wiped. let dry for approximately 10min, then apply primer/sealer and paint,. No need for a etch primer, you just wiped the etch on.
NOTE: might want to use a little flex agent to help with rock chips.
Hope this helps, I just painted a brand new Dodge 3500 front chrome grill this way 6 months ago and still looks fabulous.
Hope things go well, if you decide to paint.
Matt