Protect your hands by wearing gloves when cutting the peppers and when rubbing the chicken with marinade. Plan ahead so the chicken can marinate overnight; allowing it to come to room temperature before grilling makes for faster and more even cooking.
Variation: Alternatively, preheat oven to 350 degrees. Lightly oil a 10-inch cast-iron skillet; place skillet over medium-low heat. Add about 5 pieces of chicken to skillet, skin sides down. (Be careful not to overcrowd the skillet.) Discard used marinade. Cook, brushing occasionally with reserved cup fresh marinade and turning, until well browned on all sides, about 30 minutes. Transfer chicken to a baking dish; set aside. Wipe out skillet. Brush skillet with more oil, and cook remaining chicken in 2 more batches, transferring cooked chicken to the baking dish. Brush chicken generously with more marinade, and transfer to oven. Bake until cooked through, about 15 minutes.