Heat oven to 400° F. Drizzle ½ tablespoon of the oil in a roasting pan. Remove the zest from the lemon in thin strips; set aside. Thinly slice the lemon. Place half the slices in the pan.
Place the chicken on top of the lemon slices and season with 1/8 teaspoon of the salt.
Slice each zucchini in half lengthwise, then slice each half into ¼-inch-thick half-moons. In a bowl, combine the zucchini, parsley, and pepper and the remaining oil, lemon slices, and salt; toss.
Spread the mixture around the chicken and sprinkle the Feta over the top.
Roast until the chicken is cooked through, 15 to 20 minutes. Transfer it to a cutting board and cut each piece into thirds.
Divide the chicken, zucchini mixture, and lemons among individual plates and sprinkle with the zest.