How to Make It
Heat the oven to 375°. In a small glass or stainless-steel bowl, combine 2 tablespoons of the wine and 1/2 teaspoon of the dried tarragon. Set aside.
Coat the chicken with the olive oil and arrange the pieces, skin-side up, in a large roasting pan. Sprinkle the chicken pieces with the remaining 1 tablespoon wine and season with 1/4 teaspoon salt and 1/8 teaspoon pepper. Top each piece of chicken with a piece of the butter.
Cook the chicken for 15 minutes and then sprinkle with the remaining 1 1/2 teaspoons tarragon. Baste the chicken and cook until the breasts are just done, about 20 minutes longer. Remove the breasts and cook the legs until done, about 5 minutes longer. Remove the roasting pan from the oven; return the breasts to the pan.
Heat the broiler. Baste the chicken and then broil until the skin is golden brown, about 2 minutes. Transfer the chicken to a plate.
Pour off the fat from the roasting pan. Set the pan over moderate heat and add the reserved wine-and-tarragon mixture and the water. Bring to a boil, scraping the bottom of the pan to dislodge any brown bits. Boil until reduced to approximately 3 tablespoons, about 3 minutes. Add any accumulated juices from the chicken and a pinch each of salt and pepper. Spoon the sauce over the chicken.