Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper.
Trim the ends off the Brussels sprouts and cut them in half lengthwise.
In a large bowl, toss the sprouts with olive oil, garlic powder, sea salt, and black pepper until evenly coated.
Spread the sprouts on the baking sheet in a single layer and roast for 20 minutes until tender and charred on the edges.
While the sprouts roast, dice the chicken breast into bite-sized pieces and slice the prosciutto into thin ribbons.
Heat a large non-stick skillet over medium-high heat and cook the chicken until golden brown and cooked through.
Add the prosciutto to the skillet during the last 3 minutes of cooking, stirring frequently until it becomes crispy.
Remove the roasted Brussels sprouts from the oven and add them to the skillet with the chicken and prosciutto.
Drizzle the balsamic vinegar over the mixture and toss for 1 minute until the vinegar reduces into a light glaze.
Serve immediately while the prosciutto is crisp and the sprouts are hot.