So, you don't rinse the soap off the chrome, you just wipe it off?

That's correct. The soap almost acts like a paste polish.
As I said, just for a quick shine. But it really does work.
Let me know if you give it a try. (:
Cream

If it is true chrome, buffing with the shinny side of tin foil will work. Takes love bugs off of chrome on auto great. Just wet a little and make sure you are buffing with shinny side out.

I soak paper towels in white vinegar and then wrap the stainless fixtures (bathroom & kitchen) with them. The soppy towels fit exactly to the contours of the fixtures. I leave them on overnight, take off next day and dry & buff the stainless with a clean, non-linty cloth.

This method works very well for getting all the scummy stuff out from between the fixtures and the wall behind them.