In a bowl, combine the oil, lemon juice and zest, garlic and red and black peppers. Place the chicken in a glass dish, and douse with about half the marinade. Salt the chicken and cover with plastic and refrigerate. Allow to sit for at least three hours and up to a day.
Cook the chicken in a pizza oven (or on the grill): remove from the marinade, allowing the excess to drip off. Grill bone-side down for 20 minutes, then flip and grill skin-side down for 10 minutes. Meanwhile, mix the parsley into the reserved marinade.
Remove chicken from grill and brush immediately with excess marinade.