Preheat oven to 450 degrees. Spread pesto on chicken, top with cheese and roll into a spiral, securing with toothpicks. In skillet, heat 2 tbsp. EVOO over medium; cook chicken until evenly browned, about 6 minutes. Bake in oven, 8 minutes. In bowl, toss greens with vinegar and remaining EVOO; season. Serve chicken with salad.