Rub chicken with oil and season with salt and pepper. Grill or broil chicken until browned and no trace of pink remains in the center, 3 to 4 minutes per side.
Combine lettuce and croutons in a large bowl. Toss with Caesar Salad Dressing and divide among 4 plates. Cut chicken into 1/2-inch slices and fan over salad. Top with Parmesan curls. Serve immediately, with lemon wedges.
Make Ahead Tip: The dressing keeps, covered, in the refrigerator for up to 2 days.
Tip: To make parmesan curls, start with a piece of cheese that is at least 4 ounces. Use a swivel-bladed vegetable peeler to shave off curls.