Combine all ingredients except the chicken and lime juice in a food processor and puree until pretty smooth. Place the chicken and lime juice in a mixing bowl and pour about half of the jerk sauce over it, tossing the chicken around to coat it well. Place in a container and pour the remaining sauce on top of chicken. Cover and refrigerate for at least 4 hours or overnight.
Preheat oven to 350 degrees F.
Remove the chicken pieces from the jerk marinade and place them, skin side up, on a rimmed baking sheet or dish. Bake in the oven for 45 to 55 minutes until cooked through and the juices run clear when pierced with a fork.