In a large shallow baking dish, mix the lemon zest, lemon juice, oregano, salt, pepper, and rosemary. Place the chicken in the dish, turning to coat each side. Cover and marinate up to 3 hours in the refrigerator.
Preheat your grill on high. You can also you a cast iron stove top grill for this recipe.
Thread the chicken, onion wedges, and green bell pepper pieces alternately onto skewers. Grill skewers until the chicken is no longer pink and juices run clear.