Cut chicken breasts into bite-sized pieces. in a shallow dish blend together flour, salt, and black pepper.
In another small dish add milk, and beat 1 egg into the milk until well you have a uniform mixture.
Place Panko bread crumbs into another shallow dish. Dredge chicken into the seasoned flour, shake off excess flour, then dip chicken into the milk and egg wash. Dredge chicken with Panko breadcrumbs. (Optional if you can not find Panko breadcrumbs, you can dredge the chicken nuggets back into the seasoned flour.).
Place chicken nuggets onto a wrack and let rest a couple of minutes before frying. Heat oil to 350 degrees. When the oil is hot fry several pieces at once, do not overcrowd the pan and let the chicken nuggets touch while cooking. You will need to cook these in a couple of batches. Drain chicken nuggets on a wire rack.