Not sure if your problem is really with Chlorine in the water, but here is a method used by those that brew microbial teas for plants.
they put the water in a bucket, then place it in the sunlight, and sometimes use a bubbler. the bubbles are used to oxygenate the water for the bio organisms , but I believe it also helps in the chemical process of getting rid of the chlorine.
I know this would be impractical for most people, but may be useful with those starting sensitive plants and seed starting etc.