I recall getting my Italian chrome's clearcoat off with chemical means (lacquer thinner or paint stripper) and I'd advise trying this before cutting compounds since once it's scratched it's done.
The downside to most Italian chrome is they didn't usually use the triple-plating practice of a copper layer followed by nickel and then chrome...it's often just chrome on steel (or so I'm told) so it's pretty delicate. Keep it waxed with a good quality auto wax and renew that wax regularly.