Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the cooked chicken, cream of chicken soup, sour cream, mayonnaise, cheddar cheese, and mozzarella cheese. Season the mixture with salt and pepper to taste.
Pour the chicken mixture into a greased baking dish, spreading it evenly.
In a separate small bowl, combine the crushed Ritz crackers with the melted butter, mixing until well incorporated.
Evenly sprinkle the cracker mixture over the top of the casserole.
Bake in the preheated oven for 25-30 minutes, or until the casserole is bubbly and the top is golden brown.
If desired, garnish with chopped parsley before serving warm.