Preheat the oven to 425° F.Slice the chicken through the middle horizontally, being careful not to cut all the way through the chicken. Open the chicken and spread with pesto. Add the cheese and sun-dried tomatoes. Close the chicken, covering the filling. Place the chicken in a large oven-safe skillet. Drizzle with 2-3 tablespoons of reserved sun-dried tomato oil. Season with salt and pepper. Set the skillet over medium heat, cook 5 minutes. Add 1 1/2 cups tomatoes, garlic, balsamic vinegar, and season with salt, pepper, and chili flakes. Cook 2-3 minutes, then remove from the heat.Bake for 10 minutes, until the chicken is cooked through and the tomatoes burst. Toss 1/2 cup tomatoes with basil, thyme, salt, and pepper. Serve the chicken topped with fresh tomatoes. Enjoy!