Slice all the vegetables and put them, the seasonings, and the chicken parts in your largest stock pot. Cover with 5 quarts (20 cups) cold water and bring to a boil. Simmer, with lid ajar, skimming occasionally, for 4 to 6 hours. Because reduction intensifies the flavor, do not salt the stock until you are ready to use it. Strain the stock and let it cool. Chill it until the fat on top solidifies. Remove the fat, pour the stock into containers, and refrigerate or freeze it.