To prepare the chicken, slice each of the breasts crosswise into two thin fillets. Place in a zip-lock bag and bash with a meat tenderizer or rolling pin to flatten out to about a 1/4-inch thickness.
Take two medium-sized kitchen bowls. In the first, beat the egg. In the second, combine the breadcrumbs with the garlic, pepper, and salt.
Dip each chicken fillet in the egg, then in the breadcrumb mix, and then place on a plate ready to fry.
To fry the chicken, place a large skillet over medium heat and add the vegetable oil. When the oil is shimmering, fry the chicken fillets for about 5 minutes on each side without crowding the pan (you might only be able to do 1 or 2 at a time depending on the size of the skillet). Place chicken on a plate that has been covered with a paper towel to drain any excess oil.
Serve hot, with lemon wedges on the side.