In a large resealable plastic bag, combine the vinegar, oil, lemon juice, garlic and lemon-pepper; add chicken. Seal bag and turn to coat; refrigerate for 30 minutes.
Drain and discard marinade. Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack. Grill, covered, over medium heat or broil 4 inches from the heat for 5-7 minutes on each side or until a meat thermometer reads 170°.