Pound the chicken between parchment to an even 3/4-inch thickness.
Whisk the oil, lemon juice, garlic, oregano, salt and pepper, then coat the chicken and refrigerate for 30 minutes.
Preheat a clean grill or grill pan over medium-high heat and lightly oil the grates.
Remove the chicken from the marinade and let the excess drip away before placing it on the hot surface.
Cook for 5 to 7 minutes per side without repeatedly moving it, until browned and the thickest center reaches 165°F.
Rest the chicken for 5 minutes before slicing so the juices stay in the meat.