Heat oven to 400° F. Season the chicken with ¼ teaspoon each of the salt and pepper.
Heat 1 tablespoon of the oil in a large ovenproof skillet over medium-high heat. Cook the chicken for 2 minutes per side.
Transfer the chicken to the oven and roast for 8 minutes.
Meanwhile, in a second skillet, over medium heat, heat the remaining oil. Cook the prosciutto until crisp, 1 to 2 minutes per side. Transfer to a plate.
Add the zucchini, garlic, and remaining salt and pepper to the skillet and cook until tender, about 3 minutes.
Add the prosciutto and zucchini mixture to the skillet with the chicken, squeeze the lemon over the top, and toss. Divide among the plates.