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I can't give specific recommendations, but look for a shop that does automotive rechroming. they should be used to small jobs (e.g., emblems). There should be plenty in Chicagoland.

Try Strramwood Plating - 630/830-6363, 1545 Brandy Pkwy, Streamwood, IL. I had a couple of vintage Vespa parts re-chromed a few years back and he was willing to do small jobs. The parts came out beautifully - he even polished out some of the pitting.

If you're really brave, you can DIY it with a kit since it sounds so small...

http://www.caswellplating.com/kits/index.html

Some ideas if the rust is just on the surface...

http://forum.doityourself.com/biking-bicycles/63935-rusted-chrome-parts.html

Otherwise, it looks like there are lots of places that do rechroming in Chicago, though they'll generally specialize in automotive stuff. A google search brought up a ton, you might ask at a body shop for a specific recommendation.

If they rusted in a shower, it seems that they are not damp location approved and I would think you'd want to replace the whole lamp since I'm led to believe that there may be rust inside the fixture as well.

Alsacorp sells a 3 part chrome kit in spraycans, but uh, its about $150. Only worthwhile if you plan on chroming a lot of random stuff I suppose? (the gallery on the site has chromed SHOES hahaha)

it's here: http://www.alsacorp.com/products/killercans/kc/killerchrome.htm