Preheat an outdoor grill to medium-high. Make sure the grates are clean so the chicken doesn't stick.
Arrange a chicken breast between two sheets of plastic wrap. On a work surface, using a meat mallet or small heavy pan, pound the chicken evenly until it is 1/4-inch (6 millimeters) thick. Remove the plastic wrap and transfer to a baking sheet; repeat with the remaining chicken breasts. Brush both sides of each chicken cutlet lightly with oil.
Combine the salt, pepper and garlic powder in a small bowl and sprinkle evenly over both sides of the chicken cutlets. Place the chicken cutlets on the grill and cover the grill. Cook for 3 to 4 minutes. Flip and spread a few tablespoons marinara sauce over each cutlet and top with a couple pieces of mozzarella and 1 tablespoon Parmesan. Cover the grill and cook until the cheese is melted and the chicken is cooked through, 3 to 4 minutes longer. Serve hot.