Place the chicken breasts in a shallow dish and add the olive oil and lemon juice. Set aside while preparing the dressing.
Place all the ingredients for the Caesar dressing into a tall measuring cup or bowl. Using an immersion or stick blender, process until smooth and creamy. Refrigerate while grilling the chicken.
Preheat an indoor or outdoor grill. Remove the chicken from the oil and lemon juice and shake off the extra marinade. Place the chicken breasts on the hot grill/griddle and season with salt and pepper. Grill until the chicken is cooked through. Remove from the pan and cut into strips for serving.
Separate the clean lettuce leaves and plate them individually or cut into bite sized pieces and add to a large salad bowl. Add the chicken, shaved Parmesan, walnuts and plenty of fresh ground black pepper. Drizzle with the Caesar dressing and serve immediately.