If your chicken hasn't been cooked already, browning it will deliver more flavor. Roast it in the oven for 30-40 minutes on a greased or parchment-paper-lined baking sheet. To do it on the stovetop, heat a tablespoon of oil in a large stockpot and sear the chicken until browned.
Add the onions, garlic, carrots, celery, parsley, thyme, and bay leaves, and saute for about 2 minutes. If they start burning, add a little water and scrape up all the bits (affectionately called fond).
Add about 20 cups of water or whatever your pot will hold. Optionally, add a tablespoon of vinegar to extract collagen from the chicken bones better.
Bring to a boil, reduce the heat to low, and simmer uncovered for 3-4 hours. Add water as needed.
Allow it to cool, then strain the stock through a fine mesh strainer into a large bowl or pot. Discard the chicken bones and meat (you could use the chicken, but it will be tasteless by now).