Mix the flour, salt, garlic powder and pepper in a shallow bowl. Dredge the chicken in the flour mixture and shake off excess.
Heat 1 tablespoon oil and 2 tablespoons butter in a 12-inch pan or skillet over medium-high heat until shimmering. Fry 2 of the chicken breasts until golden-brown on both sides (about 3 to 4 minutes per side). Transfer to warm plate, tent with foil and keep warm.