The vinegar lends a kick to the stock, but it may be omitted, if desired. A 3 1/2-pound chicken will yield about 4 cups of cooked chicken.
Combine first 8 ingredients in a large Dutch oven; add water. Bring to a boil over medium heat. Reduce heat; simmer, uncovered, 40 minutes or until chicken is done. Remove chicken from cooking liquid; cool. Remove meat from bones, and reserve for use in the following recipes. Return bones to cooking liquid; stir in vinegar, if desired. Partially cover and simmer 1 hour.
Strain the stock through a sieve into a large bowl, and discard the solids. Cover and chill the stock for 8 hours. Skim the solidified fat from the surface of the stock, and discard.
Note: Reserved meat from chicken will keep 3 days in an airtight container in refrigerator or 3 months in freezer.