Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Peel the sweet potato and cut it into 1/2-inch cubes. Cut the chicken breast into bite-sized pieces of similar size.
In a large mixing bowl, whisk together the olive oil, minced garlic, rosemary, thyme, sea salt, and black pepper.
Add the sweet potato cubes to the bowl and toss thoroughly to coat, then spread them in a single layer on the prepared baking sheet.
Roast the sweet potatoes for 10 minutes.
While the potatoes roast, toss the chicken pieces, broccoli florets, and sliced bell peppers in the remaining herb oil in the bowl.
Remove the baking sheet from the oven, add the chicken and vegetable mixture, and toss everything together.
Return the sheet to the oven and roast for an additional 15-20 minutes, or until the chicken is cooked through and the vegetables are tender and slightly browned.
Serve immediately while hot and aromatic.