Mince scallions, garlic and pepper; put in a large bowl. Squeeze 3 tablespoons juice from limes and add to the bowl with the allspice, oil, 1 teaspoon salt and 1/4 teaspoon pepper. Put chicken in bowl, turn to coat and marinate 30 minutes.
Heat broiler. Put chicken on broiling pan, reserving marinade. Broil the chicken 4-6 inches from the heat source, basting it occasionally with reserved marinade, until browned and cooked through, about 30 minutes.