Toss chicken with oil, garlic, salt and pepper; refrigerate, covered, 30 minutes. In a small bowl, whisk together vinaigrette ingredients; refrigerate, covered, until serving.
Grill chicken, covered, over medium heat until a thermometer reads 165°, 5-7 minutes per side. Let stand 5 minutes before slicing.
Place greens on a serving plate; top with chicken, blueberries and mandarin oranges. Whisk vinaigrette again; drizzle over salad. Top with cheese.
