Combine the oil, vinegar, prunes, capers, oregano, olives, garlic, bay leaves, 1/4 teaspoon salt and a few grinds of pepper in a large shallow baking dish. Add the chicken and turn to coat. Cover with plastic wrap and marinate at least 1 hour or overnight.
Preheat the oven to 375 degrees F. Using a slotted spoon, remove the chicken from the marinade to a plate. Pour the marinade into a 9-by-13-inch baking dish. Arrange the chicken on top, skin-side up. Sprinkle the brown sugar over the chicken breasts and pour the white wine around them.
Bake, basting three or four times with the pan juices, until the chicken is crispy on top and cooked through, 1 hour to 1 hour 20 minutes.
Transfer the chicken, prunes, olives and capers to a serving platter. Moisten with a few spoonfuls of the pan juices and sprinkle generously with the parsley. Pour the remaining pan juices into a sauceboat and pass with the chicken.