The Urban Legend that blondes have more fun and that chlorine turns blonde hair green is not a 100% true
It is not the chlorine that causes the hair to turn green, but it is tiny particles of copper sulfate which turns blonde or even white hair a greenish color or tint. What the chlorine does to most peoples hair is to make it look rather dull and dry because it removes some of the oils in the hair.
Chemically copper compounds are often found in pool algicide chemical treatments to help prevent algae from developing in a pool; just part of the regular cleaning and maintenance of a pool. Copper in the pool water gets oxidized by the chlorine, which then sticks to the outer covering of a hair shaft or binds to the proteins in an individual strands of hair. Producing a greenish look to the hair.
Statue of Liberty
When copper oxidizes it will turn a greenish color. We see this at the Statue of Liberty, on copper pennies and copper pipes. Basically just a chemical reaction.
To help reduce getting green hair, try wetting your hair with regular tapwater just before you go swimming. This will help reduce the amount of pool water being absorbed by your hair. Wear a swimming cap (note most blondes turn this idea down). Another tip is to take a spray bottle of water with a a few drops of hair conditioner in it and spray on your hair just before entering the pool. Finally, shampoo your hair, right after swimming.
Checking the chemical balance of the pool water can help reduce this issue, and possibly changing the type of pool chemicals may help as well.