Spread the tomato sauce onto the bottom of a 10-by-15-inch baking dish. Heat 2 tablespoons of the oil in a large nonstick skillet over medium heat. Place 4 chicken cutlets in the skillet; cook until golden, 1 to 2 minutes on each side. Using a spatula, transfer the browned chicken cutlets to the baking dish, placing them on top of the sauce. Repeat with the remaining oil and chicken cutlets.