To a large pot add the chicken, onion, carrots, celery, garlic, bay leaf, thyme, peppercorns and water to cover, about 14 cups. Bring to a simmer over medium-high heat. Skim the top of the broth of any impurities rise to the surface. Adjust the heat to maintain a gentle simmer. Simmer the broth, uncovered, for 1 hour, skimming as needed.
Remove the chicken to a plate. Continue to simmer the broth. Use tongs to handle and shred the meat of the chicken and set aside for another use. Return the bones and skin to the broth and continue to simmer for an additional hour.
Remove from the heat and strain the broth. Discard the bones and vegetables and allow the broth to cool. Refrigerate for up to 4 days or freeze for up to 3 months.