Separate the chicken into individual breasts. Butterfly the breasts by cutting into the center but not completely through, until, when opened, the breast lies flat. Place the butterflied chicken breasts in a large rectangular baking dish. Pour in the eggs and completely coat the chicken. Cover and let stand in the refrigerator for at least 1 hour but up to 12. Periodically rotate the chicken breasts in the egg mixture.
Put the breadcrumbs on a large plate and mix in the salt and pepper. One by one remove the chicken breasts from the eggs and lightly coat both sides in the breadcrumbs. Place the pieces on a rack while you continue with the remaining chicken breasts.
In a large skillet over medium-high heat, melt 2 tablespoons of the butter and 1 tablespoon of the olive oil until bubbling but not browning. You will have to cook the chicken in two batches. Lay half of the chicken breasts in the pan, without crowding, and cook until golden brown, 3 to 5 minutes. Turn the chicken over and cook 3 to 5 minutes more. Transfer the chicken to a baking sheet and keep warm in the oven while you cook the second batch in the remaining 2 tablespoons of butter and tablespoon of olive oil.
Serve the chicken with a wedge of lemon and a sprinkling of salt and pepper.