Heat oven to 450° F. Place the chicken on a baking sheet; season with ¼ teaspoon each salt and pepper. Place the prosciutto on a second baking sheet. Roast until the chicken is cooked through and the prosciutto is darkened, 6 to 8 minutes.
Meanwhile, steam the broccolini in a steamer basket in a large saucepan until tender, 3 to 5 minutes. Toss with the olive oil and ¼ teaspoon each salt and pepper in a medium bowl.
Top the chicken with the prosciutto. Serve with the broccolini and lemon wedges.