In a medium mixing bowl, whisk together the balsamic vinegar, olive oil, honey, minced garlic, oregano, and thyme until the honey dissolves completely into a smooth mixture. Season with salt and pepper to taste.

Place the chicken breasts in a large resealable plastic bag or shallow dish, then pour the marinade over them, ensuring each piece is thoroughly coated. Seal the bag or cover the dish with plastic wrap, then refrigerate for at least 30 minutes, though 2 to 4 hours produces the best results.

Preheat your oven to 400°F (200°C). Remove the chicken from the refrigerator and let it sit at room temperature for 10 to 15 minutes to ensure even cooking.

Line a baking dish with aluminum foil or parchment paper and lightly grease it with olive oil. Arrange the marinated chicken breasts in the dish, spacing them at least an inch apart, and pour any remaining marinade over the top.

Bake for 25 to 30 minutes, or until a meat thermometer inserted into the thickest part of the chicken reads 165°F (75°C) and the chicken shows a golden-brown caramelized exterior. For extra moisture and flavor, baste the chicken with the pan juices after 12 to 15 minutes of baking.

Remove the chicken from the oven and let it rest for 5 to 10 minutes before slicing. Slice into thick pieces, arrange on a serving platter, drizzle with pan juices, and garnish with fresh basil if desired.