Whisk together olive oil, lemon juice, vinegar, and dried herbs. Add cut vegetables to a bowl and toss with 2 Tablespoons of the olive oil mixture. Set aside
Add cubed chicken to a glass bowl and cover with remaining olive oil mixture. Cover and place in refrigerator to marinate for 2 hours. You could marinate in less time, the flavor just won't be as intense.
Alternate vegetables and chicken while threading on skewers[if using wooden skewers you can soak in water to prevent burning will on grill.
Season with salt and pepper.
Grill, rotating until all sides are slightly browned, chicken is cooked, and vegetables have softened.
Serve with basil sauce.