In a food processor, pulse the scallions, chiles, vinegar, thyme, garlic, allspice, salt, and pepper to a thick paste.
Transfer the paste to a large bowl, add the chicken, and toss to coat. Let stand for 10 minutes.
Position an oven rack in the center of the oven and heat the broiler to high. Line the bottom of a broiler pan with foil and replace the perforated top part of the pan. Oil the pan or coat with cooking spray. Arrange the chicken on the broiler pan. Season generously on all sides with salt.
Broil the chicken in the center of the oven, turning once after about 10 minutes, until fully cooked and nicely browned in spots, about 20 minutes total. Transfer to a platter and serve.