Put all the ingredients except the chicken drumsticks in a bowl and whisk them together.
Pour the mixture onto a large, shallow dish.
Pat the chicken pieces with paper towels.
Score each drumstick 3 times.
Put the chicken in the dish and roll each piece until it is coated with the sauce.
Cover with plastic wrap, and let marinate in the refrigerator for 1 hour.
Preheat the broiler to medium heat.
Lay the coated chicken uncut side up on a foil lined broiler pan.
Put the marinade on one side.
Broil the chicken pieces for 7-8 minutes.
Using tongs, carefully turn the chicken over and broil on the other side for 7-8 minutes more.
Turn chicken again.
Baste the chicken with half the sauce.
Broil for 5 minutes, turn, and baste the chicken with the rest of the sauce.
Broil for a final 5 minutes.