Place all ingredients, except chicken and salt, in a food processor and pulse until smooth. Pour the mixture into a large bowl. Add the chicken and turn to coat. Cover, refrigerate and marinate the chicken 4 hours, or overnight, turning occasionally.
Heat your barbecue to medium-high. Set the chicken in a barbecue-safe skillet. Brush the chicken with the jerk marinade and then season with salt. Set the skillet on one side of the barbecue. Close the lid and turn the heat off underneath the chicken; leave the other side of the barbecue set to medium-high. Barbecue the chicken for 50 to 60 minutes, basting occasionally, or until the temperature in the deepest part of the thigh registers 185°F (85°C) on a meat thermometer. Transfer the chicken to a plate, tent with foil, rest 10 minutes, and then carve.