Heat the olive oil in a large, heavy skillet over medium heat and cook the onions and garlic, stirring, until wilted, about 7 minutes. Add the tomatoes and season with salt. Simmer, covered, until the sauce begins to thicken, about 20 minutes. Add the vinegar and simmer another 5 minutes.

Preheat the oven to 350F/170C. Season the chicken with salt and pepper. Place the parts in a ceramic or ovenproof glass baking dish and pour the sauce over and around the chicken parts. Add enough water so that the liquid comes about a third of the way up the chicken. Bake until tender, 45 to 55 minutes, basting every 15 minutes or so to keep the meat moist. Ten minutes before removing from oven, add the cheese cubes to the dish. The cheese should be in oozing chunks when the dish is served. Serve hot, accompanied by feta mashed potatoes.