Remove and discard giblets and neck from chicken. Rinse under cold water; pat dry. Trim excess fat. Place chicken, 16 cups water, and remaining ingredients in a large Dutch oven or stockpot; bring to a boil. Cover, reduce heat, and simmer 2 hours. Remove chicken; let cool. Remove and discard skin. Remove chicken from bones; shred with 2 forks to measure about 3 cups meat, reserving meat. (Store chicken in an airtight container in refrigerator; reserve to use in soup or for other uses.) Strain broth through a paper towel-lined sieve into a large bowl; discard solids.
Cover and chill stock overnight. Skim solidified fat from surface of stock; discard.
Note: Stock may be frozen in airtight containers for up to 3 months.