Place chicken, vegetables and water in a large stockpot. Cook on high heat until you begin to see bubbles break through the surface of the liquid. Turn heat down to medium low so that stock maintains low, gentle simmer.
Skim the scum from the stock with a spoon or fine mesh strainer every 10 to 15 minutes for the first hour of cooking and twice each hour for the next 2 hours. Add hot water as needed to keep bones and vegetables submerged. Simmer uncovered for 6 to 8 hours.
Strain stock through a fine mesh strainer and pour into a heatproof container, discarding the solids.
Place in refrigerator overnight. In the morning, remove solidified fat from surface of liquid.
Use the stock in recipes or drink as-is.