Place the oil, vinegar, basil, thyme, garlic, salt, and pepper, and garlic in the bowl of a food processor. Process until well blended. Place the chicken breasts in a large bowl or container and pour the marinade over, turning the chicken to coat it well. Refrigerate for at least 3 hours and up to 12 hours.
When ready to cook, preheat the grill or build a charcoal fire.
Remove chicken from the marinade. Grill the chicken, turning once, until browned and just cooked through, about 4 minutes per side (an instant-read thermometer should read 165 F). Transfer the chicken to a cutting board and slice.
Notes
The roasted garlic in this marinade adds a soft smoky garlic flavor, but if you were not in the mood to roast that, or are just out of time, add a teaspoon or two of finely minced garlic in its place. If you’re adding it raw, you need a lot less, as it has much more bite when it’s uncooked.