Combine chicken, onion, carrots, celery, garlic, thyme, and bay leaf in a large stockpot; pour water into the pot. Bring to a gentle simmer over medium-low heat, being careful not to let the mixture come to a boil. Once simmering, skim off any foam or impurities that accumulate on the surface of the water and reduce the heat to low.

Gently simmer the mixture on low for 12 hours, skimming off any foam as needed.

Remove stockpot from heat and let cool for 1 hour.

Pour stock through a fine strainer and transfer to food-safe containers.