Preheat your oven to 400°F (200°C) and preheat your grill to medium-high heat.
Peel and dice the sweet potato into 1/2-inch cubes, and chop the bell pepper and zucchini into similar-sized pieces.
On a large baking sheet, toss the diced vegetables with half of the olive oil, the balsamic vinegar, and a pinch of salt and pepper.
Roast the vegetables in the oven for 25-30 minutes, tossing halfway through, until the sweet potatoes are tender and caramelized.
While the vegetables roast, whisk together the remaining olive oil, rosemary, thyme, garlic powder, salt, and pepper in a small bowl.
Coat the chicken breast thoroughly with the herb marinade on both sides.
Place the chicken on the grill and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F.
Remove the chicken from the grill and let it rest for 5 minutes to lock in the juices before slicing.
Serve the sliced herb chicken alongside the roasted vegetable medley.