Preheat oven to 425°F. Line baking sheet with parchment. Divide Parmesan cheese into 12 circles on prepared baking sheet. Bake 5 to 8 minutes or until cheese melts and turns golden brown. Immediately remove from oven and cool for 1 minute. Gently remove crisps using metal spatula and place on wire rack to cool completely. Can be made 2 days ahead and stored at room temperature in a closed container.
Remove chicken from marinade and grill until thoroughly cooked. Toss remaining ¼ cup Caesar Dressing with lettuce. Serve chicken and Parmesan crisps over lettuce. Sprinkle with additional Parmesan and drizzle with additional Dressing.