Clorine is not stable in solution in water. letting is stand for 24 hours usually gets rid of most of it. Des' suggestion of aeration is an accelerator to the process by increasing the surface area, not really by substituting oxygen, as that would be an extremely transient effect.
Chloramines, on the other hand, don't go nowhere, and are not a good thing.
What Camille indirectly brought up is the alkalinity of the water - it's ability to withstand pH change by acids - is quite important, and is actually a stronger player than pH alone. If you have a head for it, and really want to learn more about all of this go to my website and read Dr. Bill Argo's 5-part series on
Plant Nutrition
Some folks rely on relatively inexpensive RO systems to produce pure water for irrigation, as that allows them to control the chemistry quite precisely. Yeah, there's an initial investment, but on a per-gallon basis, it's cheaper than anything besides collected rainwater.