Thread skewers with boneless, skinless chicken breast cubes, pieces of romaine lettuce hearts and baguette cubes; season. Preheat a foil-lined grill to medium. Grill, turning occasionally, until chicken is cooked through and lettuce and bread are charred in spots, about 10 minutes. During last 3 minutes of grilling, brush with some Caesar dressing. Drizzle with additional Caesar dressing and top with shaved Parmesan.