Place chicken in a resealable plastic bag set in a large bowl.
Drain pineapple, reserving 1/4 cup juice. Combine pineapple, reserved juice, and next seven ingredients. Pour mixture over chicken; seal bag. Marinate in the refrigerator for 2 to 24 hours, turning bag occasionally. Drain, reserving marinade.
Prepare grill for indirect grilling. Test for medium heat above drip pan. Place chicken, bone sides down, on grill rack over drip pan. Brush with some of the marinade. Cover and grill for 50 to 60 minutes or until no longer pink, turning and brushing once with about 1/4 cup marinade.
Combine the remaining marinade and cornstarch. Cook and stir until bubbly. Cook and stir for 2 minutes more. Serve over chicken.