Just a piece of advice I have learnt in my days of fooling about with cars.
Don't EVER use metal polish on a chromed surface. It actually scratches the chrome allowing moisture to get to the metal underneath, causing what you are trying to avoid.
Any furniture polish will be able to clean and shine your chrome without being abrasive.
Metal polish is for bare metal surfaces.
Simon.
I agree about not using metal polish. A good car paint polish like the one I used is OK for chrome as it actually creates a protective coating. I used Nu-Finish polish on my Chrysler AP6 chrome for 30+ years and the guy who bought the car from me a couple of years ago wanted to know who re-chromed the bumper bars. When I told him they were original, his jaw dropped.