Prepare your marinade. Chop one of the onions and combine it with olive oil, lemon juice, garlic, salt and pepper, bay leaves and oregano. Adjust seasoning to taste. Marinate the meat in this mixture for anywhere from a few minutes to overnight in the refrigerator.
If you're using wooden skewers for your kebabs, soak them in warm water while you heat your grill. Put the cooking rack 4 inches from the heat source of your charcoal or gas grill. Cut the second onion into quarters, pull apart the pieces. Alternate the chicken and onion on the skewers. Grill the skewers 12 to 15 minutes until the chicken is cooked through (the center will be slightly pink to white). Serve with lemon wedges.