Remove and discard giblets and neck from chicken. Rinse chicken with cold water, and pat dry. Re-move skin, and trim excess fat; split chicken in half lengthwise. Place in a large heavy-duty, zip-top plastic bag, and set aside.
Combine brown sugar and next 8 ingredients in a food processor; process until smooth. Pour mixture over chicken; seal bag, and marinate in refrigerator at least 12 hours, turning bag occasionally.
Remove chicken from marinade, reserving marinade. Place marinade in a saucepan. Bring to a boil, and remove from heat. Coat grill rack with cooking spray; place chicken halves on rack over medium-hot coals (350° to 400°). Grill 20 minutes on each side or until done, basting frequently with reserved marinade. Serve with Lime Dipping Sauce, if desired.
NOTE: Sharp kitchen scissors are the safest and easiest tool for cutting the chicken in half. Substitute 3 1/2 pounds of chicken pieces for the whole chicken, if desired.