Beat the egg in a shallow dish with a fork or whisk. Dip the chicken into the egg. Coat the chicken with the bread crumbs.
Heat the oil in a 10-inch skillet over medium-high heat. Add the chicken and cook for 15 minutes or until well browned on both sides and cooked through. Remove the chicken from the skillet and keep warm.
Stir the soup, milk and water in the skillet and heat over medium heat until the mixture is hot and bubbling. Serve the chicken and sauce with the rice. Sprinkle with the cheese.