Removing rust.
 

I have a 99 Schwinn Automatic Comp Joe Garcia Signature model bike in chrome.

I haven't taken the most absolute care of it, and there is a little rust on it. What's the most effective way to remove this?

Thanks.

If it is just light surface rust, and not pitted, spray some WD40 on a rag and try to rub it off. If it's heavier than surface rust, try navel jelly (buy at hardware store and follow directions).

Naval jelly nasty stuff. Try chrome polish first. Not sure what naval jelly will do to chrome but have that feeling it ain't gonna be good.

Super fine steel wool can also do well, depending on the severity of the rust. Easy does it, of course.
I'd agree that naval jelly might be a bit much for what you need.