To make the marinade whisk together olive oil, garlic, vinegar, thyme, salt, and pepper in a 13x9 baking dish.
Pound chicken between sheets of waxed paper to 1-inch thick. Pierce the chicken breasts with a fork.
Add the chicken to the marinade and turn several times to coat. Let marinate at room temperature 30 minutes or up to 24 hours in the refrigerator.
Preheat grill to medium high heat.
Lift chicken from marinade and pat dry with paper towels. Discard the marinade.
Cook chicken undisturbed for 5 to 7 minutes per side. Turn heat down to medium-low, move chicken to an area of the grill without flame. Close lid and continue cooking until internal temperature reaches 165 F, about 5-10 minutes depending on the thickness of your chicken.
Remove from grill to a cutting board. Cover chicken with foil to keep warm and allow them to rest for 5 minutes. Slice and serve.