Step 1 Heat the oven to 375 degrees. Set aside a 4-quart casserole or baking dish.
Step 2 Combine the flour, salt, pepper and oregano in a large plastic food bag. Coat a few chicken pieces at a time, shaking off the excess.
Step 3Heat 1 1/2 of tablespoons of oil in a large nonstick skillet over medium-high heat. When the oil is hot, brown the chicken on all sides in 2 batches without crowding, about 6 minutes. As the pieces are browned, transfer to the reserved casserole. Repeat the process until all the chicken is browned, adding more oil as needed (reserve 1/2 tablespoon). Add any remaining seasoned flour to the casserole.
Step 4Add the reserved 1/2 tablespoon of oil to the same skillet over medium-high heat. When hot, add the onions, garlic, celery and carrots. Cook, stirring often, until the onions are is soft, about 8 minutes. Add the wine, tomatoes, broth, tomato paste and olives. Stir well. Bring to a boil, then pour over the chicken, making sure the ingredients are well distributed.
Step 5Bake, covered (with foil or casserole cover), 1 hour. Use tongs to move chicken from bottom to top. Bake, uncovered, about 30 minutes more. There should be lots of sauce (for spooning over the macaroni side dish). Cool, then refrigerate up to 3 days, covered airtight.
Step 6To serve, skim any congealed fat off the surface. Reheat, covered, at 350 degrees until bubbling, about 45 minutes. Taste; adjust seasoning. Serve over hot macaroni, spooning on extra sauce. Sprinkle with the parsley mixture and feta cheese. Serve hot.