Pound with a meat mallet to 1/4-in. thickness. In a shallow dish, combine the lime juice, oil, onions, garlic, 2 tablespoons dill and pepper; add chicken. Turn to coat; refrigerate, covered, 2-4 hours.
Drain and discard marinade. Grill chicken, uncovered, over medium-hot heat for 6-7 minutes on each side, or until a thermometer reaches 165 °. Sprinkle with remaining 1 tablespoon dill.