Mix chicken, 2 tablespoons oil, garlic, mint, oregano, salt, and pepper in medium bowl. Let marinate 30 minutes. Whisk remaining 2 tablespoons oil and lemon juice in small bowl to blend.
Prepare barbecue (medium-high heat). Pull off large mint leaves from stems. Alternate chicken, onion, and mint leaves on skewers; sprinkle with salt and pepper. Grill until chicken is just cooked through, turning and basting occasionally with oil-lemon mixture, about 9 minutes. Serve Greek Salad alongside.