If included, remove and discard the chicken innards. Add the chicken and the neck (if included) to a large stock pot.
Wash and coarsely chop the celery. Peel and quarter the onion. Peel and smash the garlic with the side of a knife. Add the celery, onion, and garlic to the pot. Add enough water to just cover the chicken. Add 2 teaspoons of salt and 1/2 teaspoon black pepper then stir. Simmer the chicken for 40 to 60 minutes or until cooked through, being cautious not to boil. Boiling the chicken will result it dry, tough meat.
Once cooked, remove the chicken to a plate to cool. Then remove and shred the meat, discard the skin, bones, and neck. Set the meat aside.
Strain the broth from the pot through a fine mesh strainer and set aside.
In a large Dutch oven with a tight fitting lid, add the butter and melt. Slice the sausage in 1/3-inch slices and add it to the butter. Cook over medium-low heat to just brown the sausage. Add 8 cups of the reserved broth to the pot and bring to a rolling boil. Add more salt and pepper to taste. Add the rice and stir well. Add the shredded chicken. Reduce the heat to a simmer, cover, and cook for 20 minutes, stirring once or twice, or until the rice is tender and most of the liquid is absorbed. Add additional broth if necessary. Serve immediately.