Add marinade ingredients to food processor and puree until almost smooth.
Pierce the chicken with the tip of a knife to make many tiny holes. Rub marinade into chicken and refrigerate 24 to 48 hours, depending on desired intensity.
When ready to cook, prepare a slow and smokey charcoal fire. Remove chicken from marinade. Transfer the marinade to a small saucepan. Brush chicken with oil and grill over low heat until done, about 30 minutes.