Step 1

Whisk lime juice, 1/2 cup rum, and next 4 ingredients in bowl. Place chicken in resealable plastic bag. Pour marinade over; seal bag. Turn bag to distribute marinade. Chill 4 hours, turning bag twice.

Step 2

Place lime quarters in shallow bowl. Pour remaining 2 tablespoons rum over, tossing to coat. Let stand at room temperature.

Step 3

Prepare barbecue (medium heat). Grill chicken until cooked through, about 15 minutes per side. Transfer to platter.

Step 4

Grill limes until soft and slightly charred, about 5 minutes. Garnish platter with mint sprigs. Squeeze grilled limes over chicken and serve.