Congrats on the new ride!
I used some paint reducer to clean up the chrome strip, it actually did a great job at restoring it to a high shine. Just lightly rub it lengthwise with the reducer. Try not to touch the surrounding [blue] paint. The strip is clear-coated - which is what you are cleaning up.
Be very carefull as the reducer will actually dissolve the paint coating if you aren't carefull. I just gave mine a couple quick wipes with the reducer and a clean rag. You don't want to remove the protective clear-coating. Good luck.
Nathan
