Bring first 8 ingredients to a boil in a Dutch oven. Reduce heat, and simmer 1 hour or until chicken is done. Remove from heat; let stand in broth 1 hour.
Remove chicken, and cool slightly; reserve 1 2/3 cups broth. Skin and bone chicken, and cut into bite-size pieces.
Bring chicken, reserved broth, and rice to a boil in a large saucepan. Cover, reduce heat, and cook 20 minutes or until broth is absorbed and rice is tender. Remove from heat; let stand 5 minutes. Fluff with a fork.