Preheat the Oven. Preheat your oven to 175°C (350°F).
Prepare the Chicken. Pound the chicken breasts to an even thickness using a meat mallet or rolling pin. This ensures even cooking.
Season the chicken breasts with salt and pepper to taste.
Assemble the Dish. Place the chicken breasts in a greased 23x33 cm (9x13 inch) baking dish.
Top each chicken breast with slices of Swiss cheese, ensuring they are fully covered. Make the Sauce: In a medium bowl, combine the condensed cream of chicken soup and milk. Stir until well mixed.
Pour the soup mixture evenly over the chicken and cheese.
Add the Stuffing: Sprinkle the dry herb stuffing mix over the top of the chicken and sauce.
Drizzle the melted butter evenly over the stuffing.
Bake: Cover the baking dish with aluminum foil and bake in the preheated oven for 50 minutes.
Remove the foil and bake for an additional 10 minutes, or until the chicken is cooked through and the stuffing is golden brown.
Serve: Let the dish cool slightly before serving. Serve the Swiss chicken with your choice of sides, such as rice, mashed potatoes, or a fresh salad.