Preheat your oven to 400°F and line a large rimmed sheet pan with parchment paper for easy cleanup.
Trim the woody ends off the Brussels sprouts and slice them in half vertically; cut the chicken breast into uniform 1-inch bite-sized pieces.
In a small mixing bowl, whisk together the olive oil, balsamic vinegar, honey, minced garlic, sea salt, black pepper, and dried rosemary until well combined.
Place the chicken and Brussels sprouts onto the prepared sheet pan and pour the balsamic dressing over them, tossing thoroughly to ensure every piece is coated.
Spread the ingredients out into a single layer, turning the Brussels sprouts cut-side down to ensure they get a deep golden sear against the pan.
Roast in the center of the oven for 20 to 25 minutes, tossing halfway through, until the chicken is cooked through and the sprouts are tender with crispy, charred edges.