In a bowl, mix the softened butter with mustard, chopped tarragon, and minced garlic.
Carefully loosen the chicken skin by sliding your fingers between the skin and meat. Spread the butter mixture under the skin, covering as much of the breast and thighs as possible.
Cut the lemon in half and stuff it inside the chicken cavity.
Rub the outside of the chicken with olive oil and season generously all over with salt and pepper.
Place the chicken in a roasting pan and roast at 425°F/218°C for 20 minutes.
Reduce the temperature to 375°F/190°C and add the white wine to the pan.
Continue roasting for 40-50 minutes more, or until the internal temperature reaches 165°F in the thickest part of the thigh.
Let the chicken rest tented with foil for 10 minutes before carving.
