In a large saucepan, combine 4 cups water, chicken, onion, celery, carrot, salt and pepper. Bring to a boil. Reduce heat; cover and simmer for 15-20 minutes or until chicken juices run clear and vegetables are tender. Remove and set aside chicken and carrot. Strain broth, discarding remaining vegetables. Set aside 1/2 cup chicken broth. (Discard or save remaining broth for another use.)
In a bowl, combine stuffing mix and butter. In a microwave-safe bowl, whisk together the soup mix and the remaining water. Microwave, uncovered, on high for 1-1/2-2 minutes, whisking occasionally. Add sour cream and reserved broth. Stir soup mixture into stuffing mixture. Place half the stuffing mix in a greased shallow 5-cup baking dish; top with reserved chicken and carrots, then peas. Cover with remaining stuffing mix. Cover and bake at 350° for 20-30 minutes or until heated through.