Remove any giblets from the chicken and place it in a large stockpot (at least 8 quarts).
Add the carrots, celery, onions, garlic, peppercorns, bay leaves, and thyme to the pot with the chicken.
Pour in about 12 cups of cold water, or enough to fully cover the chicken and vegetables by 1 to 2 inches.
Set the pot over medium-high heat and slowly bring it to a gentle boil. This typically takes 20-25 minutes. As the broth begins to heat, skim off and discard any foam or impurities that rise to the surface.
Once boiling, reduce the heat to low so the liquid simmers gently. Cover partially with a lid and cook for 1 to 1 1/2 hours, or until the chicken is tender and cooked through to an internal temperature of 165°F.
Using tongs, carefully transfer the chicken to a large bowl or platter to cool slightly.
Strain the broth through a fine-mesh sieve or cheesecloth-lined colander into another large pot or heatproof bowl. Discard the cooked vegetables, herbs, and peppercorns.
Once the chicken is cool enough to handle, remove and discard the skin and bones. Shred the cooked chicken meat and refrigerate it for another use, such as soups, casseroles, or salads.
Use the broth immediately, or let it cool to room temp before refrigerating.