Add ¼ cup of the vinaigrette to the rice mixture and toss.
When ready to serve, spoon the rice mixture onto 4 plates lined with soft lettuce leaves. Slice the chicken diagonally into thin strips; arrange atop the rice. Drizzle with the remaining vinaigrette and serve immediately.
Grill the chicken and prepare the rice mixture in advance; cover and refrigerate separately. Assemble the salads and drizzle with the remaining dressing just before serving.