Preheat oven to 350 degrees F. Place herbs and apple into cavity of chicken, tie legs together and place in roasting pan. Pour 1 cup stock and cider around chicken. Roast chicken for 18-20 minutes for each pound (about 2 hours for a six pound bird).
Peel celery root and cut into 1/2-inch dice. Cut apple into thirds lengthwise, and then cut each third in half crosswise. Season with salt and pepper.
Add the second cup of stock to the roasting pan about one hour into roasting time. Ten minutes later, scatter vegetables around chicken. Sprinkle herbs, salt and pepper onto chicken. Add chestnuts. With a large spoon, turn vegetables to coat in pan juices. Baste chicken.
In a small bowl, place softened butter and add flour. With the back of a spoon, press butter against the side of the bowl to combine well. All flour should be incorporated into butter to form a paste or a beurre manie. Reserve.
Chicken is done roasting when an instant-read thermometer inserted in the deepest part of the thigh registers 180 degrees F. Remove chicken from oven and place on a carving board. Cover with foil. Remove vegetables from pan and reserve. Note: Vegetables should be tender. Place back in oven if not soft when pierced with a fork.
Place roasting pan on stovetop, add 1/2 cup stock and 1 cup apple cider and bring to a boil. Adding a little at a time, whisk butter/flour mixture into liquid. Whisk or stir until sauce is smooth and slightly thickened.
Carve chicken, serving vegetables alongside. Spoon pan gravy over chicken.