This is really a handy little trick to try to spruce up chrome. All you need to do is get a small piece of aluminum foil. Turn the shiniest side out. Now dampen the chrome with water and rub with the foil to polish.
You will soon notice, as you start to polish the chrome with your tin foil, the area will turn black. This is normal. But once you're done, your chrome will regain a shine, almost like new!
Instead of water, you could also substitute some cola beverage to the section for something that needs more drastic attention. However, I advise to wear your rubber gloves because you could develop a rash if you are sensitive and prone to allergies. Then proceed to polish with foil in the same fashion.