Chrome is beautiful, but very delicate and easily damaged. Cleaning tip for cleaning all your chrome (including faucets, wheels, bumpers, etc) is to be gentle and use very neutral cleaners. Dish soap and clean microfiber rags will usually be all you need. For chrome that has been neglected for a while, try white vinegar or peroxide cleaner, then buff dry. Also, waxing your chrome with a carnuba wax will protect and also make it easier to clean.
Check out more cleaning tips and how tos on our How to Clean Series Blog.