Wash the chicken and remove the fat from the cavity. With a large knife or Chinese cleaver cut off the legs at the point where the thigh and drumstick meet the breast, then cut down the side of the chicken, so that the back comes of the breast. Cut the back and breast in half.
Place the chicken in a pot, add the water and bring to a boil. Reduce the heat and simmer slowly for 25 minutes, skimming frequently. When the scum no longer rises to the surface, turn the stock down until the surface is just moving and simmer for another 2 hours.
Strain the stock in a cheesecloth lined fine strainer. Discard the chicken and strain the stock again. This stock will last for up to 3 to 4 days in the refrigerator, or it can be frozen for future use.