Place the flour, black pepper and cayenne pepper in a gallon size zip lock bag.
Dip chicken one piece at a time into egg white, allowing excess to drip off. Place chicken one at a time in the bag with flour mixture, shake the bag to lightly coat, remove the chicken and set aside.
Add oil to an oven-safe skillet, turn to medium heat. Oil is the right temperature when a pinch of flour dropped in sizzles. Do NOT allow oil to get to the smoking point.
Brown chicken on both sides, about 8 minutes on each side. Leave chicken in skillet and place in the oven, do not cover. Cook 30 minutes. Place chicken on paper towels to remove excess oil.
Notes
There should be about 3/4 cup flour remaining after coating chicken. Also, about 1/2 the oil will remain after chicken is removed from skillet. This is so much healthier than deep frying chicken...and tastes great too!