Make jerk marinade: Process chiles, onion, scallions, garlic, and thyme in a food processor until mixture forms a coarse paste. Add brown sugar, allspice, salt, nutmeg, cinnamon, vinegar, soy sauce, lime juice, and oil; season with pepper. Process until smooth. Marinade can be refrigerated in an airtight container up to 1 day before proceeding.
Transfer 1/3 of the marinade (about 1 cup) to a small bowl; set aside to use for brushing chicken. Transfer remaining marinade to a large bowl. Add chicken; toss to coat, rubbing marinade under the skin and all over chicken. Cover with plastic wrap, and refrigerate overnight. Allow the chicken to come to room temperature before grilling.
Heat a grill to low (if using a charcoal grill, coals are ready when you can hold your hand 5 inches above grate for 7 seconds). Brush grate lightly with oil. Place chicken on grill, skin sides down. Discard used marinade. Grill chicken, brushing occasionally with reserved cup of fresh marinade, until the skin sides are well browned but not charred, about 25 minutes. Turn chicken, and continue to cook, basting it occasionally, until cooked through, 20 to 25 minutes. Cut chicken breast halves into 2 or 3 pieces, if desired. Serve with lime wedges. ,
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.