Pat chicken dry and pound chicken if some parts are too thick. Combine the olive oil, lemon juice, oregano, garlic, salt and pepper in a bowl or resealable freezer bag. Add chicken and toss well to combine. Marinate for at least 30 minute
Preheat grill or grill pan to medium high heat. Place chicken on the grill for 5-7 minutes. Use tongs to flip over and cook until juices run dry, approximately 5-7 more minutes. Discard extra marinade
Remove chicken from the grill. Sprinkle with parsley and serve with lemon wedges and vegetables, if desired.
Storage: Store any leftovers in an airtight container. They will last up to 4 days.