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Mythbusters proved that the best solution for taking rust off of chrome was good old fashion coke~a~cola and foil. (i cant remember if it was tin foil or aluminum foil)
Bar Keeps Friend and Windex. Sprinkle the BKF on a Magic Eraser, spray it with some Windex and rub the rust away. Dont do this every time as it is somewhat abrasive but it sounds alot better than Coke and Tin foil.