Set the chicken's backbone aside for another 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 to 5 minutes. Turn the pieces and continue cooking about 4 minutes. Pour off the fat from the skillet. Add the wine, thyme and bay leaf. Cover closely and cook about 15 minutes. Uncover and transfer the chicken pieces and onions to a warm serving dish. Remove and discard the bay leaf and thyme sprigs, if used. Add the butter to the wine sauce and swirl it around until melted. Pour the sauce over the chicken and sprinkle with the chopped parsley.