I grew up with Schwinn bikes during that time period. The chrome was always low quality and rusted easily. The kids in the neighborhood removed the rust with a Brillo pad until we stopped caring. It wasn't all that much work. I don't know if it left the chrome looking like-new, so I'd test it on a small spot before doing the entire bike.
If it's a bike that you want to keep in "vintage" condition, I'd consider clear lacquer on the chrome.