In a large, shallow, non-metallic dish, arrange the chicken in a single layer. Mix together the lemon juice, oil, garlic, oregano and cayenne in a small bowl. Stir well to thoroughly combine.
Pour the mixture over the chicken and turn to coat both sides. Let stand at room temperature for 20 minutes or cover and refrigerate for up to 6 hours.
On a greased grill, cook the chicken over hot coals for 4-5 minutes on each side or until the meat is no longer pink inside. Discard the marinade.