Preheat a grill to medium. Stir the ketchup and juice of 1 lime in a small bowl; set aside. Mix 2 tablespoons jerk seasoning paste, 2 tablespoons brown sugar and 1 tablespoon vegetable oil in a medium bowl. Add the chicken and turn to coat. Mix the remaining 1 tablespoon seasoning paste, 1 tablespoon brown sugar and juice of 1/2 lime in a small bowl. Microwave 30 seconds to dissolve the sugar; stir and set aside.
Cut the plantains in half lengthwise and toss in a bowl with the scallions, remaining 1 tablespoon vegetable oil, 1/2 teaspoon salt and a few grinds of pepper.
Lightly oil the grill grates. Grill the chicken, turning once or twice, until charred and cooked through, 10 to 12 minutes. Grill the plantains and scallions, turning, until charred and tender, 4 to 5 minutes.
Brush the jerk-lime mixture on the chicken. Roughly chop the plantains and scallions; toss together. Serve the chicken with the plantain mixture, lime ketchup and lime wedges.