Cooling and diluting over-reduced stock down with cold water
I have to ask, why would you want to add water? Chicken stock should simmer 8 hours. That is the optimal time to extract all flavours. What you have there is (probably) perfect. However, if you don't want as much flavour, add the water later, not now. Also, to cool, the best way to do it is in an ice bath or a cold water bath (one where there is a constant slow source of running cold water).