Make marinade: in a large baking dish, whisk together oil, garlic, vinegar, thyme, 1 teaspoon salt, and 1/2 teaspoon pepper. Add chicken; turn several times to coat. Let marinate at room temperature 10 minutes and up to 30 minutes.
Lift chicken from marinade and grill until browned and cooked through, 2 to 3 minutes per side. Remove from grill. Cover half of chicken with foil to keep warm. Reserve other half for grilled chicken cobb salad.