Preheat the oven to 220°C.
Mash the butter, two-thirds of the tarragon, salt, pepper, and garlic together in a bowl.
Rub the herb butter inside and all over the outside of the chicken in a roasting tin.
Pour the wine into the tin and roast in the oven for 15 minutes.
Reduce heat to 190°C and roast for 40 minutes, basting occasionally with pan juices.
Check that juices run clear, then let the chicken rest for ten minutes with the oven off.
Stir the remaining chopped tarragon and extra seasoning into the roasting juices.
Carve the chicken and serve immediately drizzled with the pan juices.