This can also be adapted for pork, seafood or even tofu. For the best flavor, try using whole allspice berries and black peppercorns and crush them with the bottom of a heavy pot or in a coffee mill before adding to the food processor.
skin-on bone-in chicken leg quarters or (3 lb) chicken, cut into quarters
Place all ingredients except oil and chicken in a blender or food processor. With the processor running, slowly add a thin stream of oil until the mixture becomes thick. Save 1/2 cup of the marinade for drizzling over chicken during cooking.
Place chicken and larger amount of marinade in a ziptop plastic bag and marinate for at least 2 hours or overnight in the refrigerator.
Prepare the grill.
Remove chicken from marinade, discard marinade. Place chicken on the grill, searing the first side (about 3-5 minutes). Turn, drizzle with reserved marinade, and sear the other side. Move chicken to an area of indirect heat (such as the grate above the grill or off to the side) and cook until it reaches an internal temperature of 165 degrees. Use a grill pan on the stovetop, if preferred.