In a large stockpot, combine all the ingredients. Slowly bring the water to a simmer and skim off any scum that appears. (It sounds awful and doesn’t look much better, but it’s nothing to worry about.) Reduce the heat, cover, and cook for 25 minutes. Check occasionally to make sure that the water is just barely moving, and adjust the heat as necessary. Turn off the heat and let it stand covered until cool, about 2 hours. Remove the chicken from the pot to a large cutting board or platter (to catch the juices), and pull off the meat, discarding the skin and bones. The only way to do this is with your fingers.
Strain the stock, discarding the solids. Refrigerate it to chill it. Remove and discard the congealed fat, which will have risen to the top. If you want to concentrate the flavor, transfer the stock to a clean pot, bring it to a boil, and reduce over high heat to about
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