Preheat oven to 400°.
Wash and dry chicken inside and out then dry well. Fit chicken into a roasting pan (you want no more than 1" of space on any side of the chicken otherwise the juices will burn).
Mix together onion, carrot, celery, lemon zest, and 1/2 of the minced herbs. Loosely stuff cavity with some of the ingredients, place the remainder on the bottom of the roasting pan and place chicken on top of the aromatic vegetables.
Mix remaining minced herbs with butter. Gently separate the chicken skin from the breast meat and carefully rub herb butter on breast under the skin.
Rub the chicken with lemon olive oil and season with salt and pepper. Squeeze lemon over chicken and place rind into cavity. Insert probe thermometer into thigh and set for 165 degrees. Pour half of the wine and chicken stock in the bottom of the pan and place, uncovered in hot oven.
Baste after 1/2 hour, if you don't have enough juice in pan use some chicken stock. Do not cover bird until browned and then loosely place foil over breast. If wings start to brown to early wrap with foil.
Remove chicken to a warm plate and loosely cover with foil. Let rest for 10 minutes before carving.
Remove some of the fat in the pan by using a paper towel or ice cubes. (Dredge the paper towel through the juices to pull out some of the fat or pour off the juices into a heat proof measuring cup. Add a few ice cubes; the fat will stick to the cold cube, discard cube. You may have to do this several times).
Put the roasting pan on top of the stove over medium-high heat and bring a boil, add remaining wine and stock scraping the fond (the yummy pieces stuck to the pan) from the bottom of the pan. Reduce by half, add demi-glace if using and serve with chicken.