The mojito, a cocktail of rum, lime and mint lends its flavor to this fruity and tangy barbecue sauce. Boneless and skinless chicken thighs are terrific grilled, as they are less likely to dry out than chicken breasts.
Berry Mojito Sauce
Heat oil in small saucepan over medium-low heat. Add shallots, cover and cook, stirring occasionally until softened, about 2 minutes. Add blackberries, blueberries, lime juice, molasses, brown sugar, teaspoon salt and red pepper. Bring to a simmer over medium heat. Cook, stirring often, until reduced to about 1½ cups, about 6 minutes. Remove from heat. Stir in rum, mint, and lime zest. Cool. Set aside 1/4 cup sauce for brushing over chicken.
Prepare a medium-hot fire in an outdoor grill. For a gas grill, preheat on high, then adjust to medium-high (about 450°F). For a charcoal grill, let coals burn for about 15 minutes after white ashes form on surface, and you can hold your hand just above cooking grate for about 3 seconds.
Season chicken with salt and pepper. Lightly oil grill grate. Place chicken on grill and close cover. Grill, turning occasionally, until golden brown and cooked through, 12 to 14 minutes. During the last 3 minutes, brush both sides with reserved sauce. Serve hot with remaining sauce.