Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Wash and peel the sweet potato and carrots, then dice the sweet potato into 1/2-inch cubes and slice the carrots into rounds.
Cut the chicken breast into uniform 1-inch pieces to ensure they cook at the same rate as the vegetables.
Place the chicken, sweet potato cubes, carrots, and broccoli florets into a large mixing bowl.
Add the olive oil, minced garlic, dried rosemary, dried thyme, sea salt, and black pepper to the bowl, tossing thoroughly until everything is evenly coated.
Spread the mixture in a single layer on the prepared baking sheet, making sure not to overcrowd the pan so the vegetables roast rather than steam.
Roast for 20 to 25 minutes, tossing the ingredients halfway through, until the chicken is cooked through and the sweet potatoes are fork-tender.