Remove and discard giblets and neck from chicken. Rinse chicken with cold water; place chicken in an 8-quart stockpot. Add celery and remaining ingredients; bring to a simmer. Reduce heat, and simmer 45 minutes; skim surface occasionally, discarding solids.
Remove chicken from pot; cool. Remove chicken breast meat from bones; reserve for another use. Return chicken to pot; bring to a boil. Reduce heat, and simmer an additional 2 hours, skimming surface occasionally.
Strain stock through a sieve into a large bowl; discard solids. Cool stock to room temperature. Cover and chill 8 to 24 hours. Skim solidified fat from surface; discard. Refrigerate remaining stock in an airtight container for up to 5 days or freeze for up to 3 months.