I have a bathroom light fixture that over the years has developed a considerable amount of rust from all the steam and condensation. is there a way of removing/reducing the rust without scratching the chrome surface? Some type of non-abrasive cleaner?

I would try a product called THE WORKS. It cuts rust and lime deposits away
uhh…scrape it?
You can try using Naval Jelly. Let it soak in, then rub with a cloth.
Use Chrome Polish by Turtle wax (Auto supply). It will take the rust off and protect it from future rust. If the chrome is already pitted you will still see the compromised finish but it should take the rust away. If you have really stubborn rust use some very fine steel wool.
If you have rust, isn’t a few scratches a MOOT point…….Not proper English but you get the point..
For a chrome surface try a pre polish prep and then follow with a metal polish to bring back the chrome shine and it will look as good as new, http://www.corrosionconnection.com/index.aspx?pageid=530. That is the link to the specific page.
I found both of these on a new website called http://www.corrosionconnection.com
I hope this helps!