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Whisk all ingredients together in a bowl.
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Place drumsticks in half the pineapple juice mixture in a large resealable plastic bag; refrigerate 1 hour.
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Reduce remaining mixture in a saucepan over medium-high heat until thickened; set aside for basting.
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Preheat grill to high.
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When hot, turn off one burner, leaving the other lit.
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Remove drumsticks from marinade.
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Arrange on UNLIT portion of the grill.
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Cook chicken to an internal temperature of 165 degrees (about 40 minutes).
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Baste with reserved glaze regularly.
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Turn after 20 minutes; continue basting until done.