Combine olive oil, bourbon, lime juice, sugar, Cajun seasoning, chipotle and cilantro. Reserve 1/4 cup of the marinade, set aside. Pour the remaining marinade into a resealable plastic bag with the chicken. Marinate for 1 hour.
Preheat grill or broiler to medium. Brush grill racks with small amount of oil to prevent sticking. Remove chicken from marinade, discard marinade. Place chicken thighs bone side down and cover. Grill for 5 to 7 minutes. Turn the chicken skin side down. Grill 5 to 6 more minutes. Turn thighs to skin side up; baste the tops with the reserved marinade. Grill 3 to 4 more minutes, until internal temperature reaches 165ºF or juices run clear.