Preheat grill to medium-high heat. Brush chicken lightly with oil; season with oregano, salt and pepper. Grill 3-4 minutes per side, or until cooked through. When cooked, top each breast with a spoon of pasta sauce and slice of mozzarella cheese. When cheese is melted, sandwich chicken and lettuce in panini buns. Serve remaining pasta sauce in small bowls alongside for dipping the burgers in.