If desired, gently separate the skin from each breast and slide a tarragon sprig underneath the skin of each breast. Stuff the bird with the quartered lemon wedges and tarragon sprigs, giving the lemons a squeeze once they are inside the cavity. Place the chicken on its side in the baking dish. Roast uncovered for 20 minutes. Turn the chicken to the other side and roast for another 20 minutes. Reduce heat to 350 degrees. Turn the chicken breast side down (tail in the air) and roast for another 20 minutes. Turn the chicken breast side up and continue to roast until done. Cooking time will vary depending on the size of the bird. A small chicken will roast in about 1 1/4 hours; a larger will take 1 1/2 hours or more. When done, the juices should run clear and the leg joint should move easily.
Remove chicken from baking dish and cover loosely with foil. Turn off the oven and place inside, with the door ajar.
Preparing the sauce: Keep juices in the baking dish and skim half the fat off the top and discard.
Over moderate heat add a handful of crushed walnuts and cook for 2 to 3 minutes, scraping and stirring the bits that have accumulated on the bottom of the dish. Do not burn.
Add the wine and a splash of white wine vinegar and bring to a boil. Reduce the heat to low and simmer until thickened, about 5 minutes.
While the sauce is thickening, remove and discard the lemons and tarragon from the chicken and carve chicken into large pieces. Place on a warm platter and spoon the sauce over the chicken while all is still hot.