Season chicken breasts on both sides with salt and pepper. Place flour, beaten egg, and panko crumbs into separate shallow dishes. Coat chicken breasts in flour, shaking off any excess; dip into egg, and then press into panko crumbs until well coated on both sides.
Heat oil in a large skillet over medium-high heat. Place chicken in the hot oil, and fry until golden brown, 3 or 4 minutes per side. Transfer to a paper towel-lined plate to drain.
