Preheat the oven to 400 degrees F (200 degrees C).
Place chicken in a large pot and cover with water. Season with salt and pepper. Bring to a boil; reduce heat, cover, and simmer until chicken is no longer pink in the center, about 15 minutes. Drain and let cool, 5 to 10 minutes. Chop chicken into small pieces.
Mix together chopped chicken, canned vegetables, chicken soup, onion, sour cream, water chestnuts, and cheese in a large bowl until well combined; pour into a 9x13-inch baking dish. Sprinkle crushed crackers over the top and dot with butter.
Bake in the preheated oven until filling starts to bubble and topping browns, about 30 minutes.
