Heat the oil in a large stockpot over medium-high heat. Add the onion; ] sauté until colored and softened slightly, 2 to 3 minutes. Add the celery and carrot and cook until the celery has begun to get tender, another 3-4 minutes. Transfer the mixture to a large bowl.

Add half of the chicken pieces to the pot; sauté both sides until lightly browned, 4 to 5 minutes. Transfer the cooked chicken to the bowl with the vegetable mixture. Sauté the remaining chicken pieces. Return the vegetables and chicken pieces to the pot. Reduce the heat to low, cover, and cook until the chicken releases its juices, about 20 minutes.

Increase the heat to high; add the water, salt, and bay leaves. Bring to a simmer, then cover and barely simmer until the stock is rich and flavorful, about 30 minutes.

Strain the stock and discard the solids. Cool the stock (ziploc bags filled with water and frozen make great stock-coolers), then place in a container in the fridge until cold, and all the fat rises to the top and sets. Skim off the fat, then you may keep the stock in the fridge for up to 2 days, and in the freezer for 6 months.

Makes about 2 quarts of stock.