Removing rust from steel Bertoia dining chairs  

Right here....
is your best rust destroyer, as long as the rust isn't completely through the metal.

You can get noxon at any Ace Hardware. It's about $7 a bottle. It's ammonia based, and is about 10 x as potent as brasso. I restore metal all the time, and you can't beat it. If the rust is too deep, you can use your thumbnail under a towel with noxon applied, or use a very small flat head screwdriver in conjunction with the noxon to get down close, and lightly scrape off the outer rust shell exposing the rust dust underneath for a deeper, more extensive cleaning, and polishing.
Rust is not a cancer in the sense that it will keep deteriorating if there's no humidity. The dry atmosphere will snuff it out, not allowing it to continue. Cleaning it with Noxon, and keeping it out of the humidity, will ensure it will last almost forever with very little to no further deterioration.

onegroovydude, thank...onegroovydude, thank you for your helpful and kind response!

U CAN ALSO TRY
steel 'wool' type 00000 for getting the rust off and polishing it a little. works great most of the time. available at most DIY stores

Steel wool
would not be better than noxon IMO. Steel Wool actually leaves very light swirl marks/fine scratches when used on metal, plated metal, glass, or just about anything. You are actually inviting more oxidizing and rust to begin once this has been done. Bronze, or brass wool (because it is softer than metal and plated metals) does not scratch, and would be better than steel. All would need to be wet to use, but IMO steel wool would not be my number one (or number two, or three for that matter) choice for any metal where you're trying to polish, and/or end oxidation.
Steel Wool will begin to oxidize (rust) over time all by itself, and this can cause it to scratch even more. Just the slightest moisture or humidity can cause Steel Wool to begin oxidizing, and it's often hardly noticeable to the naked eye. I would steer clear of that in this situation, and stick with the noxon and a towel, or a very worn scrubbing pad that won't dig into the metal, just to add a little texture to the scrubbing power. It's really your best offense, and defense.