Rinse the chicken and pat it dry with paper towels. Season the chicken with 1/4 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 to 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 the remaining salt and pepper and cook until tender, about 3 minutes. Transfer the prosciutto, zucchini, and garlic to the skillet with the chicken, squeeze the lemon over the top, and toss. Divide among plates.