I painted the chain ring on my winter bike. It was chrome plated (the more common modern thin flash chrome, not the old fashioned mirror-like chrome), which I scuffed with medium grit sand paper to help the paint adhere. I did mask off the outer edge and teeth, which makes it look similar to the wheels (which are painted black with machined brake surfaces). Its held up so far, but I've taken care to minimize the chance of damage. See below:
I've painted a couple with good results. I generally go over it with angle grinder and a flap disc first.
This one I originally painted for my RRBBO1 bike and has since been on several bikes and has the most miles. Held up well.
Cool, that is kinda what I thought would be the case, that it would wear with contact with chain but be good on rest of it. Thanks for all the fast responses!!