Wash the chicken pieces, and dry well with paper towels. Trim the tips from the chicken wings and discard. Season the chicken pieces very generously and thoroughly with the salt.

Heat the butter in a heavy Dutch oven or heavy pan over moderately low heat until it becomes frothy but not brown. Add the chicken pieces to the pot, and with a wooden spoon toss them about to coat them with the hot butter.

Cook slowly, turning the pieces occasionally, until they are a pale-golden color, about 5 minutes. Add the onion and celery to the pot, stir to combine, and cover tightly.

Reduce the heat to very low, and cook this way for approximately 20 minutes.

At the end of 20 minutes, 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.

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 30-45 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 completely, covered, for 10 minutes before serving.

Note: For a more refined dish you may choose to leave the onion and celery whole and remove them along with the back and neckbone pieces before adding the rice