To a food processor add lemon zest, lemon juice, garlic, red pepper, chiles, parsley, paprika, red wine vinegar and oil. Process until it becomes a paste. Season with salt and pepper. Reserve 1 cup of the sauce as set aside for garnishing cooked chicken later.
Divide chicken pieces into 2 large resealable plastic bags. Divide the marinade into both bags and seal. Turn the chicken around in the bags to distribute the marinade. Place chicken in the refrigerator and let it marinate for at least 1 hour and up to 1 day.
Preheat grill to medium-high heat.
Remove chicken from bags with tongs and drain well. Season with salt and pepper. Place on grill, skin side down first, and grill for about 15 minutes on each side turning occasionally until cooked through. (You might need to do it in batches if grill is not big enough.) Serve with lemon wedges and the reserved piri piri sauce.