I have the same thing at my school. I Brita everything I drink because it's just soooo bad. I can't afford to buy that much spring water, so before I hauled my fish up, I tested my dechlorinator on the water and the readings went from dangerous levels of chlorine to no chlorine detectable. I let it sit for awhile before adding it, too, so the dechlorinator has time to work on the whole bucket. I use Prime. *poses with bottle and flashes pearly whites at the cameras*
Seriously though, if your tests come up clean, I'd say you can go for it. If you're nervous, though, then I'd say wait for the month to be up.