I didn't believe the following method when I read it but after trying it out I can confirm it works really well.

Take a piece of aluminum kitchen foil and screw it into a ball. 
Soak the ball of foil in clean water.
Put on a pair of rubber gloves to stop your hands getting stained
Scrub the rusty leg with the foil and watch with amazement as the rust dissolves! Re-dip the foil ball in water as needed and replace when necessary.

I'm not sure what the science is but I think it is something to do with a chemical reaction between the aluminum and the iron oxide.

The foil seems soft enough not to scratch the chrome but certainly takes off the rust.  It's a very cheap, easy and safe method.