In a bowl or pitcher, combine the olive oil, balsamic, garlic, parsley, basil, salt and pepper. Whisk until the marinade is emulsified.
Place the chicken in a large zip bag and pour in half the marinade. Seal the bag and set it aside.
Place the tomatoes and green beans in a separate zip bag, and pour in the rest of the marinade. Seal the bag and marinate both bags in the refrigerator for up to 2 hours (or make it right away-- but it would best to marinate for at least a little bit).
Preheat the oven to 425℉. Arrange the chicken and veggies on a sheet pan, and discard any marinade left in the bag. If you want to make your clean-up easier, line the sheet pan with parchment paper.
Roast for 25 minutes, gently shaking the pan once during that time. The chicken should be cooked through and the vegetables starting to brown nicely. Sprinkle with Parmesan cheese, sprinkle with fresh parsley and serve.