We took an old chrome chair that was quite rusty and tried cleaning it with various products.
Just paint thinner and steel wool did a fairly decent job, although you have to be careful to not scratch the chrome. But this put on no protection against rust coming right back.
Care polishes and other rust removers generally had a wax with them to give them some protection. We were successful in making the chair frame better looking and in getting rid of some rust, but certainly not all of it, especially where the rust had actually gone right through the chrome.
To get this chair re-chromed would cost about $60, more than the price of this cheap chair, unless of course this is a 1950's irreplaceable piece.