Arrange 1 large lettuce cup and 1 small lettuce cup on each plate, overlapping slightly. Spoon the chicken salad into the lettuce cups. Drizzle more vinaigrette over the salads. Sprinkle with the Parmesan and serve.
Do-Ahead Tip: The chicken salad can be prepared 4 hours ahead and refrigerated. Just before serving, spoon the salad into the lettuce cups.