Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Cut the chicken breast into 1-inch cubes and place them into a large mixing bowl.
Prepare the vegetables by peeling and cubing the butternut squash, halving the Brussels sprouts, and cutting the broccoli into bite-sized florets.
Add the prepared squash, sprouts, and broccoli to the bowl with the chicken.
Mince the garlic clove and add it to the bowl along with the olive oil, dried rosemary, sea salt, and black pepper.
Toss all ingredients together thoroughly until the chicken and vegetables are evenly coated in the oil and spices.
Spread the mixture in a single layer across the prepared baking sheet, ensuring there is space between pieces to allow for roasting rather than steaming.
Roast for 20 to 25 minutes, tossing the ingredients halfway through, until the chicken is cooked through and the vegetables are tender with golden-brown edges.