Combine all the ingredients in a big stock pot and place over high heat.
When the liquid comes to a boil, decrease the heat to med-low, cover the pot and simmer, skimming the surface occasionally, until the chicken is falling off the bone, 1 ½ to 2 hours.
Let stand and cool to room temperature.
Strain the broth through a large sieve or colander into a bowl or plastic container.
Use a wooden spoon to press the chicken and vegetables against the sieve to extract as much of the broth as possible (may reserve chicken and vegetables for another use).
Cover the container and place in the refrigerator until thoroughly chilled and the fat has hardened on the surface, at least 8 hours or preferably overnight.
Use a slotted metal spoon or spatula to remove all of the fat from the broth.
Divide broth into 2 or 3 smaller containers and store in the refrigerator for up to 5 days or freeze for up to 3 months.