WHISK together the ingredients for the marinade and pour into a gallon-sized ziploc bag. Add the chicken and marinate in the refrigerator for at least 30 minutes.
PREHEAT oven to 375°F. Place the chicken in a baking dish and pour any of the remaining marinade on top. Bake for 25-30 minutes, until the internal temperature reaches 165°F.
WHILE the chicken bakes, bring a pot of water to boil and add 1 tbsp of sea salt and 1 pinch of baking soda (this keeps the green beans bright green and nice texture). Boil the green beans for 5-8
minutes, until fork-tender - do less time if you want them more crisp. Drain the green beans.
IN a large bowl, whisk together the olive oil, balsamic vinegar, minced shallot, salt, and pepper. Add the green beans, cherry tomatoes, and feta cheese to the bowl and toss until everything is well coated with the vinaigrette.
WHEN the chicken is done baking, broil for 2-3 minutes to crisp the skin, if desired.