Place the chicken in a dutch oven cover with 6 cups of water. Bring to a simmer, then reduce to medium heat.
Add onion, carrots, celery, garlic, and bay leaves, then cover and cook for 1 hour.
Remove the chicken from the dutch oven and set aside. Add the rice to the dutch oven, then cover and cook for an additional 30 minutes.
Remove the chicken bones and chop the chicken into 1/2-inch pieces.
Remove from heat, add the chicken, salt, and pepper, and stir. Remove the bay leaves before serving.