In a medium bowl, combine the balsamic vinegar, honey, a tablespoon of olive oil, garlic, thyme, rosemary, chili flakes, salt and pepper. Stir well to mix.
Place the chicken breasts in a resealable plastic bag and pour the marinade over the top. Seal and toss the chicken to evenly coat. Marinate for at least 30 minutes.
While the chicken marinades, place the potatoes and cherry tomatoes on a sheet pan. Drizzle with the remaining olive oil, season with salt and pepper, and stir to coat. Bake for 25 minutes.
Remove the sheet pan from the oven and toss the green beans with the potatoes and tomatoes.
Remove the marinated chicken breasts from the plastic bag, reserving the remaining marinade in the bag. Place the marinated chicken, evenly spaced, on top of the vegetables. Pour the marinade from the bag over the top of the chicken and vegetables.
Return the sheet pan to the oven. Bake for 30 to 40 minutes, periodically basting the chicken breasts with the pan juices, until the internal temperature of the chicken reaches 165 degrees
Allow the chicken to rest for 5 to 10 minutes. Spoon the pan juices over the top of each chicken breast before serving.