Place chicken pieces in a large pot and cover with 6 cups water; bring to a boil. Using a large spoon, remove the white foam from the top of the water.
Add in the sliced onions, celery pieces, and carrots; cover the pot, lower to medium-low heat, and cook for 30 minutes.
Preheat the oven to 375ºF.
Spread the uncooked rice on the bottom of a baking dish. You will need a baking dish that is stovetop and oven-safe.
Remove the chicken pieces from the broth and arrange them over the rice.
Pour 3 cups of broth into the baking dish with the rice and chicken. Depending on how much water was reduced while making the broth, you may need to add up to ¼-cup more rice.
Place the dish over medium-high heat. Season with salt and pepper and bring to a boil.
Remove from stovetop and place in oven; bake for 20 minutes or until all liquid is absorbed.
Remove from oven and let cool 10 minutes. Serve.