Some Mothers PowerMetal scratch removing polish, followed up by Mothers chrome polish, each applied and polished with a microfiber cloth, may be just the ticket.
PS: My maxi-scooter and Suzuki DR650 have very little in the way of any shiny bits. The scooter has a chrome exhaust shield. I polish it on occasion, but with our weather, keeping the shiny bits polished is something I more or less gave up on a long time ago.