Combine rum, lemon juice, soy sauce, sugar, garlic, jalapeno, ginger, and black pepper in small bowl.
Place chicken in resealable food storage bag.
Pour marinade over chicken. Press air out of bag and seal tightly. Turn bag over to completely coat chicken with marinade.
Refrigerate 4 hours or overnight, turning bag once or twice.
Drain chicken; reserve marinade.
Bring remaining marinade to a boil in small saucepan over medium-high heat. Boil 5 minutes or until marinade is reduced by about half.
On eight metal or soaked wooden skewers, alternately thread chicken and vegetables.
Grill kababs, uncovered, over medium-hot heat for 12-15 minutes or until juices run clear, turning and basting occasionally with remaining marinade.
To serve, drizzle marinade over chicken.