Preheat the oven to 350°F (175°C). If needed, pound each chicken breast to an even thickness for even baking.
Pour about one-eighth of the evaporated milk into a shallow bowl for dipping.
In another shallow bowl, whisk together the flour, salt, and pepper.
Dip each chicken breast into the evaporated milk, then coat thoroughly with the seasoned flour; set the coated breasts aside.
Pour the melted butter into a 9x13-inch baking dish and arrange the coated chicken breasts in a single layer in the butter.
Bake the chicken for 1 hour (60 minutes).
While the chicken bakes, combine the remaining evaporated milk, the can of cream of chicken soup, and the water in a bowl; whisk until smooth.
After 1 hour, carefully turn each chicken breast over in the dish and pour the soup mixture evenly over the chicken.
Return the dish to the oven and bake 30 more minutes, until the chicken is cooked through and golden on top.
Remove from the oven and serve the chicken with the sauce spooned over it.