Set the chickens backbone aside for later use or discard it. Sprinkle the remaining pieces of chicken with salt and pepper. Dredge lightly in flour. Shake off any excess flour.
Heat the oil in a heavy skillet large enough to hold the chicken pieces in one layer. Add the chicken pieces, skin side down, and the onions. Cook until nicely browned on one side, 4-5 min. Turn the pieces and continue cooking about 4 min.
Pour off the fat from the skillet. Add the wine, thyme and bay leaf. Cover closely and cook about 15 min.
Uncover and transfer the chicken pieces and the onions to a warm serving dish. Remove and discard the bay leaf.
To the wine sauce add the butter and swirl it around until melted. Pour the sauce over the chicken and sprinkle with the chopped parsley.