Place a watermelon slice on each of 4 plates. Spoon half of the taboule over the 4 watermelon slices in as even a layer as possible. Place another slice of watermelon over the taboule. Spoon the remaining taboule over the top slices of watermelon. Arrange the chicken slices over the taboule. Dust the chicken slices with chives and parsley. Serve immediately.