Combine vinegar, oil, garlic, basil, salt, and pepper in a large bowl. Add chicken; mix to coat. Cover with plastic wrap; refrigerate for at least 20 minutes.
Heat a cast iron grill pan over medium-high heat. Add chicken; cook until golden on the outside, no longer pink in the center, and the juices run clear, 7 to 10 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).