Place chicken breasts in a large skillet; add chicken broth. Cover and bring to a boil over high heat. Reduce heat to medium low, and simmer, covered, 30 minutes or until chicken is done. Remove chicken from skillet, and let stand 15 minutes or until cool to touch. Shred chicken.
Combine shredded chicken, celery, water chestnuts, and next 3 ingredients in a large bowl.
Stir together mayonnaise, ground red pepper, salt, and white pepper until well blended; spoon over shredded chicken mixture, stirring to coat. Cover and chill at least 4 hours.
Shrimp Salad: Substitute 3 pounds chopped cooked shrimp for chicken breasts and broth. Do not cook. Reduce mayonnaise to 2 cups and salt to 1/4 teaspoon. Proceed with recipe as directed.