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Preheat oven to 350 degrees. On a sheet of waxed paper, combine the flour and bread crumbs. In a smaller bowl, whisk together egg whites and water. Dip chicken in egg white mixture, then dredge in bread crumb mixture, turning to coat. In a large skillet, heat oil over medium high heat. Add chicken, cook, turning once, until browned, about 10 minutes. Place chicken in a shallow baking dish. Bake until cooked through, about 15 minutes. To prepare sauce, in a small saucepan over medium heat, melt margarine. Stir in flour until well combined. Slowly add milk, stirring constantly. Cook, stirring until thickened, about 8 to 10 minutes. Remove from heat; stir in 1/4 cup cheddar. Place chicken breasts on serving plates. Drizzle with sauce and sprinkle with the remaining cheddar. Serve immediately.
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