Position a rack in the upper third of the oven and preheat to 450ºF. In a large bowl, whisk together the lemon juice, oil, vinegar, oregano, garlic, and salt and black pepper to taste.
On a greased baking sheet, generously season the chicken with salt and toss to coat. Arrange skin-side down and bake for 15 minutes. Turn the chicken pieces and continue cooking until the skin is golden and crisp and the juices run clear, about 10 minutes more. Preheat the broiler to high.
Transfer the chicken to the bowl with the lemon mixture and toss to coat, then use a slotted spoon to transfer back to the baking sheet and arrange skin-side up. (Reserve the remaining liquid.) Broil until sizzling and deep golden brown, 10–15 minutes. Transfer to a platter, then pour the remaining sauce over top. Sprinkle with the parsley and serve.
