All great advice. Only thing I can add is after the shell is clean a short soak in diluted CLR. This will help remove the buildup of deposit's around the pits. You will see bubbles rising to the surface. When that slows remove and rinse well. If the chrome plating is flaking, by all means wear gloves. Ploughman is right. Jam chrome bits under the skin and it hurts!!
Creighton