Ah yes! Just the smell of this cooking clears your sinuses better than any cold medicine! This sounds like a lot of vinegar, but it really isn't. This dish has been a favorite of mine from my earliest days, and it's a big reason why I've always loved the taste of vinegar. It's a recipe from my great-grandmother, "Ma" Del Medico, who took it from Sicily and passed it on to my grandmother ("Nana" Pacitto), who in turn passed it on to Mom. And here it is, now online as we pass it on to you.
In a big cooking pot, saute (lightly fry) the onions in a little oil. Drizzle the oil around the bottom of the pan a couple of times. You only want a little oil, because you're not frying them. Cook the onions until they're translucent, when you can almost see through them and they are tender. Keep the heat on low to medium high so you don't brown the onions. It should take about 10-15 minutes on a low to medium heat. When the onions are almost ready, add minced garlic and stir.
The chicken parts need to be cut or broken into pieces, but you can leave the bones and skins in. Add the chicken pieces to the mixture, and cook in the pot until the chicken is browned.
Empty the tomato sauce into the pot. Fill the empty tomato sauce can with vinegar and pour it into the pot. Mix it all up, and add salt and pepper to taste.
Cover the pot and keep the heat on low to medium-low. Simmer for at least an hour or until chicken is fork tender; I like to let it simmer for one-and-a-half to two hours. The longer the better! If you let it simmer long enough, the chicken will become so tender it will fall right off the bone; you won't have to use a knife at all when you eat it. The smell of vinegar (which I think is wonderful) will permeate your home, but it goes away quickly once you're done cooking.
Prepare your rice in a separate pot while the chicken is cooking. White rice goes best with this dish, as it will absorb the flavor of the chicken and vinegar sauce. You can use prepared rice (such as Minute Rice) if you don't have the time or skill to properly cook rice.
Serve over prepared white rice. The sauce can be poured on top, to soak into the rice and add even more flavor.