Incidentally in a competing garden forum which I'm not allowed to link to, I found the following assertions (none with sources/ evidence attached): (the discussion was about tap water and compost tea not compost pile, but it seemed very relevant)
*Some of my local organic gurus attended that same training session with Dr Ingham and have tested San Antonio's water. What they found was that the chlorine seems to kill about 50% of the microbes[in compost tea]. Still, that leaves 50% that you would not have gotten had you not made the tea.
*Today most places are using a more stable product, Sodium hypochlorite, in place of the old, and much more dangerous liquid Chlorine. Sodium hypochlorite does not gas off from water in 24 hours like Chlorine did.
* Municipal water is chlorinated to a concentration of 2 to 10 ppm, or 2 to 10 mg per liter. Chlorine is a reactive agent, not a catalytic one. It reacts with dead plant cells just as much as it reacts with live microbes. Which is to say that the chlorine is used up by the organic matter in the water. If you dump 100 grams of biologically active organic matter into 1 liter of water, the ratio of chlorine to organic matter is 10,000 to 50,000 to 1 by weight. It would seem to me that what little chlorine is in the water is swamped by the amount of organic matter.
So in summary... we don't really know! Chlorine is in the water because it is an effective and potent bacteria-cide/ fungicide. It may or may not gas off if you let it sit for 24 hrs. It may or may not be used up by the organic matter in the pile.
I can say that in drought years, I have watered my compost pile with water direct from the hose (chlorinated) and still gotten good compost.