Heat broiler. Pat the chicken dry with paper towels, pound to an even thickness, and place on a broiler pan.
In a small bowl, combine the ketchup, molasses, 1 tablespoon of the oil, the jerk seasoning, 1/4 teaspoon salt, and 3 tablespoons water. Brush the chicken with some of the glaze. Broil, brushing occasionally, until cooked through, about 9 minutes. Discard the remaining glaze.
Brush the bread with 1 tablespoon of the oil and sprinkle with the garlic. Broil until crisp, 1 1/2 minutes. Slice the bread crosswise.
Meanwhile, heat the remaining oil in a large skillet over medium heat, add the shallots, and cook, stirring, for 4 minutes. Add the chard, 1/2 teaspoon salt, and 1/4 teaspoon pepper and cook until wilted and tender, about 5 minutes. Divide the chicken, chard, and bread among individual plates.