Preheat the oven to 425 degrees Fahrenheit (175 degrees Celsius).
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 marinates, 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.