Remove the skin from the chicken pieces, and pat dry. Sprinkle the chicken with salt and pepper.
Heat the butter or olive oil in a heavy skillet or pan. add the chicken pieces and cook about 10 minutes on 1 side, till golden brown. Turn and cook about 5 minutes on the other side.
Remove the chicken and set aside.
Add the shallots to the skillet and saute briefly. Add the tarragon and wine, and stir to dissolve the particles that cling to the bottom of the skillet.
Return the chicken to the skillet, and cover. Cook about 15 minutes at medium heat. Uncover and continue to cook at medium low heat, basting frequently, for 5 minutes, till chicken is thoroughly tender and nicely glazed.