Clear coat chips very easily off of chrome. I have heard that you can use hard furniture wax to get a really long lasting protection, or just lots and lots of turtle wax.

"If the parts are bright and shiny, they are nickel plated and chrome plated, not just chrome plated. It is true that the chrome is porous, as it is supposed to be, but the nickel is not. The nickel provides the primary corrosion resistance; the chrome keeps the nickel from tarnishing (turning yellow) and spreads the corrosive energy around so the nickel is not overloaded.

Frequent waxing not only keeps the chrome looking good, but keeps corrosive dirt off it, and can't hurt. A really good nickel-chrome plating job, though, doesn't need babying."
-finishing.com