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 mins.
Preheat grill or grill pan to medium high heat. Place chicken on the grill for 5-7 mins. Do not touch before then or else it won't cook right. Use tongs to flip over and cook until juices run dry, approx 5-7 more mins. Discard extra marinade.
Remove the chicken from the grill. Sprinkle with parsley and serve with lemon wedges and veggies, if desired.