Phil - it's interesting that this dish isn't popular in Hungary! All the Hungarian restaurants here (in Detroit) feature this as a "house special!" Boneless, skinless chicken thighs are easily available in the markets here. It wasn't always that way, but they have become a popular cut of chicken the last few years.
Roger - a more traditional version of this dish takes longer. You use whole chicken pieces - breast, leg and thigh. It starts the same by browning the chicken in butter, but then when you make the tomato sauce you put the browned chicken pieces back in (because they are not cooked through at this point), cover and simmer for a couple of hours. Then you remove the chicken, add the sour cream at the end (so it doesn't curdle) and put the sauce and chicken back together. The chicken falls off the bone...really delicous! The bones and skin add a lot of extra flavor, but the trade-off is that it takes longer. It is also served over spaetzle, a small dumpling that is made by forcing the dough through small holes over a pot of boiling water. These are also a lot of extra work to make, but so yummy with this dish.