Cut chicken into 1-inch pieces.
Mix chicken, 1 T olive oil, garlic, mint, oregano, salt and pepper in a medium bowl. Cover and marinate in the refrigerator for 30 minutes to 24 hours.
Whisk remaining 1 T olive oil and lemon juice in a small bowl.
Preheat grill to medium high heat.
Pull off large mint leaves from stems. Alternate chicken, onion and mint leaves on skewers. Sprinkle with salt and pepper.
Grill kebabs until chicken is cooked through, turning and basting with lemon-oil mixture, about 9-10 minutes.