Place the chicken, carrots, onion, celery, salt, pepper, and garlic in a large stockpot. Add enough water to completely cover the chicken and vegetables, about 4 quarts.
Bring to a boil. Skim off any foam that rises to the surface, then reduce the heat to a simmer. Cover and simmer for 1 hour.
Remove the chicken from the pot. Once cool enough to handle, remove the meat and reserve it for another recipe.
Return the chicken bones and skin to the pot. Simmer for 3–4 hours, skimming the surface as needed.
Remove from the heat and skim off any excess fat. Strain the stock through a fine-mesh sieve or cheesecloth and discard the solids.
Allow the stock to cool, then transfer it to airtight containers or freezer bags.
Refrigerate for up to 3 days or freeze for up to 3 months.