In a food processor, puree chile, scallions, garlic, thyme, brown sugar, allspice, soy sauce, lime juice, and oil. In a large zip-top bag, toss chicken with paste. Refrigerate at least 1 hour (or up to 1 day).
Heat a grill or grill pan to medium-low. Clean and lightly oil hot grill. Season chicken with salt and pepper; grill, covered, turning often to prevent charring, until cooked through, 45 to 50 minutes.