Place the chicken, onions, carrots, celery, garlic, parsley, thyme, salt, and peppercorns in a large stockpot or Dutch oven (at least 8 quarts).
Add enough cold water to cover all the ingredients by about 2 inches. The amount will vary depending on your pot, but it will be around 12 cups.
Bring the pot to a boil over high heat. Once boiling, immediately reduce the heat to low to maintain a gentle simmer.
Use a large spoon or skimmer to remove any foam or scum that rises to the surface during the first 20-30 minutes.
Let the broth simmer gently, uncovered, for 4 hours. Check occasionally to make sure it's barely bubbling, not boiling.
Remove the pot from the heat and let it cool for about 30 minutes, or until it's safe to handle.
Set a fine-mesh strainer over a large bowl or another clean pot. Carefully pour the broth and solids through the strainer.
Discard the chicken and vegetables. The broth is now ready to be used or stored.
For a clearer, less fatty broth, chill it completely in the refrigerator. The fat will solidify on top and can be easily lifted off.