Combine olive oil, lemon juice, and oregano; pour over halved chicken in a large glass baking dish. Sprinkle chicken on both sides with sea salt and black pepper. Place in refrigerator and marinate for 2 or so hours. Turn chicken at least once during marinating process.
Preheat gas grill on medium high for five minutes. Place chicken skin side down on middle of grill and turn off inner burners so that heat is indirect. Turn chicken when skin is nicely browned and continue to cook for 1-2 hours or until meat thermometer registers 170 deg F. Remove from heat, cover loosely with foil and let sit for 5 minutes before serving.