1. Place chicken breast halves between 2 sheets of plastic wrap. Using mallet or heaving pan, pound meat until it is 3/4 thick.
2
Place chicken in shallow dish. In small bowl, whisk oregano, scallions, vinegar, oil, pepper, and salt. Pour mixture over chicken and flip to coat both sides. Cover and chill about 2 hours, turning once.
3
Heat grill to medium for indirect heat. (If using charcoal grill, position coals on one half of grill. If using gas grill, heat one side to high, the other to low). Wipe grill grates with vegetable oil.
4
Remove chicken from marinade, reserving marinade. Place chicken on hottest section of grill. Cook 6 minutes, turning once. Move chicken to cooler section of grill and cook 6 minutes, turning once, until thermometer registers 165 degrees Fahrenheit.
5
Pour marinade into small saucepan and place on hottest part of grill. Bring to a boil for 5 minutes.