Start by placing the chicken breasts between two pieces of plastic wrap. Use a meat mallet to pound the chicken to 1/4 inch thickness.
In three shallow bowls, set up your dredging station: flour in the first bowl, beaten eggs in the second, and panko bread crumbs in the third.
Coat each piece of pounded chicken first in flour, shaking off excess, then dip into beaten eggs, and finally coat in panko bread crumbs, pressing gently to adhere.
Heat the oil over medium heat in a large skillet or frying pan, enough to cover the bottom of the pan.
Carefully add the breaded chicken pieces to the hot oil. Fry in batches if needed to avoid overcrowding. Cook about 4-5 minutes per side until golden brown and cooked through. Remove and drain on paper towels.
While frying, prepare the apricot dipping sauce by combining apricot preserves, natural ketchup, soy sauce, and Worcestershire sauce in a mixing bowl. Stir until blended and adjust to taste.
Slice the crispy panko chicken and serve hot with the apricot dipping sauce on the side.