Combine chicken, prunes, olives, wine, vinegar, oil, oregano, capers, garlic, chili pepper flakes, salt, and bay leaves. Cover and marinate in refrigerator at least 15 minutes and up to 24 hours. If marinating overnight, combine ingredients in a zip-top bag, seal and refrigerate.
Arrange chicken in a single layer in a casserole dish. Pour marinade over chicken. Sprinkle the sugar evenly over the chicken. Transfer the pan to the oven to bake.
Bake until chicken is cooked white throughout and top is golden-brown, 40-50 minutes.
Remove chicken pieces to a plate and top with the remaining pan juices.
Remove bay leaves before sprinkling basil over the chicken. Serve immediately.