I'll second stripping the chrome, and second using SuperClean. I use it, and it was to strip chrome that I first tried it.
I strip the chrome because it just doesn't look right, to my eye, to depict real chrome in 1:1. It's too "bright" without having the reflective quality of real chrome.
And also, there is almost always some area that needs addressing, like a sprue gate or a seam, that would damage the chrome and take more work to clean up. I find it easier just to strip it and then proceed as I normally would with assembly, priming, and painting.