Put the stock in a small saucepan, bring to a boil, and reduce by half to concentrate the flavor.
Heat the oil in a deep skillet or sauté pan large enough to hold the chicken pieces snugly. Add the onion; cook over high heat, stirring frequently, until deep golden brown, 6 to 8 minutes. It should be well colored but not burned. Reduce the heat slightly, add the paprika, and stir for a few minutes to develop the flavor.
Season the chicken pieces well with salt and pepper and add them to the pan, skin side down. Brown them well over medium high, about 7 minutes on each side. Add the reduced stock and scrape up any browned bits on the bottom of the pan. Turn the heat to low, cover the pan, and let it simmer about 15 minutes. Add the green pepper and tomato (and a little water if the pan seems dry -- Hungarians would say the chicken should almost fry instead of "swim," so don't add too much stock). Replace the lid and simmer until the chicken is very tender when pierced with a fork, about 25 minutes longer, turning the pieces once during cooking.
Transfer the chicken pieces to a dish and keep them warm while you finish the sauce. Spoon off as much grease as you can. Bring the sauce to a boil and boil for a few minutes to concentrate the flavors even more. Stir the flour into the sour cream with a fork or whisk and then whisk this into the sauce. Simmer for about 4 minutes. to cook away any floury taste and to bring the flavors together; taste and adjust the salt and pepper if necessary. Return the chicken pieces to the pan to reheat and coat them with the sauce.
Serve with boiled potatoes, rice, or the Hungarian accompaniment, which would be galushka, tiny egg noodles or dumplings that are similar to spaetzle.
You can make the paprikas up to one day ahead and refrigerate, covered. Reheat in a covered casserole dish in a 350°F oven.