Well, I would say that you can start with progressively finer grades of wet sanding paper to restore the smooth finish, then maybe try some plastic polishing compound on a mothers powerball or similar rotary ball polisher. Flitz polish works great on pretty much everything, and leaves a protective coat.
I don't know how much finish thickness you have to work with since I've never seen one of the chevy emblems up close, but that seems like it would be your only option to restore a decent finish.
But, if you're trying to paint it, wouldn't you want to leave a little bit of a rough surface? Paint needs a toothy surface to adhere to....