Heat 1 tablespoon oil in a large skillet over medium-high heat. Add 2 chicken breasts and cook, turning once, until golden brown, 1 to 2 minutes per side. Transfer to the prepared baking dish. Repeat with the remaining 1 tablespoon oil and 2 chicken breasts. Top each breast with 1/4 cup marinara, 2 tablespoons mozzarella and 1 tablespoon Parmesan.