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Put the chicken drumstick on the hottest part of the grill and cook them for 25 minutes, rotating them frequently with a pair of tongs to ensure even cooking. Step 5. Remove the chicken drumsticks from the grill and put them on a warm serving plate.
Place marinated chicken onto the hot grill and discard the marinade. To avoid flare ups, place chicken pieces between the burners as opposed to directly over the flame. Cover the grill and cook for 2 to 3 minutes, until dark grill marks appear. Flip and cook on the other side for 2 to 3 minutes. Continue flipping and cooking until the internal temperature of the chicken reaches 165 degrees F. If certain drumsticks are cooking faster than others, move them to the side or the back of the grill so that they continue cooking slowly over indirect heat.