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Step 1
Combine all sauce ingredients in a small saucepan and bring to the boil. Reduce heat to low and simmer uncovered for 30 minutes, stirring regularly. Allow to cool before mixing with the chicken.
Step 2
Place chicken in a dish or sealable plastic bag. Pour in half the sauce (or a bit more, if needed) and toss to coat all the drumsticks. Cover the dish or seal the bag and marinate in the fridge for at least 2 hours.
Step 3
Preheat barbecue to high and oil grill.
Step 4
Turn heat down to medium-low. Place drumsticks on the barbecue and grill for 20 – 25 minutes, turning regularly, until the meat easily pulls away from the bone or internal temperature reads 74° C (165° F). The barbecue sauce is sweet, so the drumsticks tend to caramelize quickly. If this occurs, move them to indirect heat to finish cooking and prevent them from burning.
Step 5
Sprinkle drumsticks with sesame seeds and chives just before serving them with the remaining sauce.