Combine egg and milk in a small bowl. Combine Parmesan cheese, bread crumbs, oregano, paprika, and pepper in a shallow dish.
Skin chicken if desired. Dip chicken pieces into egg mixture; coat with crumb mixture. Arrange chicken pieces in a greased 15x10x2-inch baking pan so pieces don't touch. Drizzle chicken pieces with the melted margarine or butter.
Bake in a 375 degree F oven for 45 to 55 minutes or until chicken is tender and no longer pink. Do not turn chicken pieces during baking. Immediately transfer chicken to a covered container; serve within 1 hour. Or cover and chill chicken; transport in an insulated container with ice packs.