Grate zucchini on holes of a box grater. Place shreds in center of a clean kitchen towel. Gather towel corners and squeeze as much liquid as you can from zucchini over a sink or bowl. Season generously with salt and pepper. Mix Parmesan and zucchini in a medium bowl and reserve.
Place each chicken breast between two pieces of plastic wrap. Pound with a mallet or large pan until ½-inch thick. Season all over with salt and pepper.
Place chicken breast on a baking sheet and brush a drizzle of olive oil onto each. Top with a thick layer of zucchini mixture. Bake in oven until just cooked through, about 12 minutes. Heat broiler to high or increase oven temperature to 500 degrees. Broil (or bake) until golden and crisp on top, about 2 minutes.
