In a large glass bowl mix lemon juice, vegetable oil, vinegar oregano, and garlic powder. Place chicken pieces in the bowl, and season with salt and pepper. Cover, and marinate in the refrigerator at least 1 hour.
Preheat an outdoor grill for high heat, and lightly oil grate
On the prepared grill, cook chicken until no longer pink and juices run clear. Periodically brush chicken with remaining marinade mixture while cooking.