Heat the oil and butter in a large frying pan over medium heat. Cook the bacon and onions until the onions start to soften.
Season the non-skin side of the chicken pieces with salt and pepper. Move the onions and bacon off to the sides of the pan and add the chicken. Season the skin side of the chicken while it browns on the first side.
When the underside of the chicken is brown, add the mushrooms, tomato, and wine to the frying pan. Bring to a boil, reduce heat, cover, and simmer until the chicken is tender. As the chicken pieces are cooked, transfer them to a bowl in the oven.
When all the chicken pieces are cooked and transferred to the oven, remove the lid from the frying pan and increase the heat to high. Reduce the sauce until thick.
Arrange the chicken pieces on individual serving plates. Mix the chervil into the sauce and spoon the sauce over the chicken pieces.