For marinade, combine all ingredients in a large, air-tight plastic bag.
Rinse thighs and pat dry with a paper towels. Add thighs to bag. Seal and refrigerate for 2 to 12 hours, turning occasionally.
Preheat grill on medium.
Meanwhile, remove chicken from marinade. Pour marinade into a small saucepan and bring to a boil over high heat. Boil for 5 minutes; set aside.
Grill chicken on covered grill for about 20 minutes, turning occasionally.
Brush bananas generously with marinade; place on grill. Grill chicken and bananas for 10 to 15 minutes, or until chicken is tender, turning bananas once. Brush chicken and bananas with marinade (after boiling it for 5 minutes) before serving.