2. Remove the lid from the pot. You will be surprised by the amount of liquid released by the chicken and vegetables. Pour in the 5 cups of water. Increase the heat slightly and cook, partially covered, for an additional 35 minutes.
3. With a long slotted spoon or tongs, remove the onion and celery and discard. For a more refined dish you may choose to remove the back and neckbone pieces as well. Taste the broth carefully. It should be highly flavored and seasoned. Indeed, it should be on the salty side, because the rice will absorb a great deal of the seasoning. Stir in the rice and cover. Continue cooking at a low simmer for 30-40 minutes longer. When most of the broth has been absorbed by the rice but the contents are still a bit soupy, remove the pan from the heat and allow to rest, covered, for 10 minutes before serving.