Prepare a grill for medium-high heat. Preheat the oven to 400 degrees F.
Add the chicken thighs to a large bowl and pour over 1/4 cup of the rum. Add the basil, rosemary, thyme, seafood seasoning, cayenne and 1 tablespoon salt. Stir to coat. Set aside.
In a small saucepan, combine the brown sugar, chipotles, butter and the remaining 1 cup rum. Simmer over low heat until the chipotles have dissolved. Remove from the heat; reserve half of the sauce in a separate bowl.
Lightly oil the grill grates. Grill the chicken until grill marks form, turning once and brushing with the sauce in the pot every few minutes, 10 minutes total. (Discard the sauce in the pot.)
Transfer the chicken to a baking sheet, cover with foil and transfer to the oven. Bake until cooked through, about 30 minutes. Brush with the reserved sauce and serve immediately.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.