Combine cooked chicken, American cheese, celery, crushed pineapple, almonds or walnuts, paprika, salt and 1/2 cup mayonnaise. Toss lightly; turn into cool pie shell.
Whip whipping cream until thick and stiff. Carefully fold in 1/4 cup mayonnaise. Spread over salad in pie shell, leaving 1 inch of salad around edge uncovered. Garnish with grated carrot. Chill until serving time at least 30 minutes. Serves 6.