Place chicken in a large pot and cover with about 5 cups of water. (An additional cup or so might become necessary during cooking process.).
Bring to boil; reduce heat, cover and simmer gently for about 30 minutes. Add carrots, celery and potatoes. Cover and continue simmering for another 30 minutes, until chicken is tender.
Remove chicken pieces from the pot, being careful to remove all bones from the pot as well. Remove meat from bones. Discard bones and return chicken pieces to the pot. (You may either discard the fat or cut it up and return it to the pot with the chicken meat.).
Stir rice into the simmering pot. Cover and allow to cook for about 20 minutes or until rice is tender and most of the liquid is absorbed.
Remove from heat. Stir well and let cool completely.
Package into meal-size portions. Freeze or refrigerate.