Free chlorine will indeed break down over time, but an hour in the fridge probably won't be sufficient - the half life of free chlorine in water is much longer

Free chlorine will indeed break down over time, but an hour in the fridge probably won't be sufficient - the half life of free chlorine in water is much longer than an hour! (In sunlight or UV, however, it'll break down much faster). Secondly, Chloramine is now often used instead (or in addition to) free chlorine. Chloramine is more stable and won't break down by putting it in the fridge. And the potential health issue isn't so much with chlorine itself anyway, but with other chemical products that can be formed by reactions with chlorine, possibly before the water even reaches your tap.