Place chicken, carrots, celery, onion, and peppercorns in a large stockpot with 3 quarts water. Bring to a boil over medium-high heat.

Reduce heat to low and simmer, uncovered, 2–3 hours, skimming foam occasionally. (After 1 hour of cooking, you may remove chicken, pick meat from the bones to reserve for another use, and return carcass to the pot.) Remove from heat and strain.