Preheat oven to 375°.
To prepare chicken, remove and discard giblets and neck from chicken; trim excess fat. Starting at neck cavity, loosen skin from breasts and drumsticks by inserting fingers, gently pushing between skin and meat.
Combine butter and next 5 ingredients (through pepper) in a small bowl. Rub seasoning mixture under loosened skin and over breasts and drumsticks. Tie ends of legs together with twine. Lift wing tips up and over back; tuck under chicken. Place carrots, celery, and onion in a single layer in a roasting pan. Place chicken, breast side up, on top of vegetables.
Bake at 375° for 40 minutes.
Increase oven temperature to 450°, and bake an additional 20 minutes or until a thermometer inserted in the meaty part of thigh registers 170°. Using tongs or insulated rubber gloves, remove chicken from pan, tilting slightly to drain juices. Let stand 15 minutes. Remove vegetables from pan with a slotted spoon; reserve.
To prepare gravy, place a zip-top plastic bag in a 2-cup glass measure. Pour wine into bag; add drippings from pan. Let stand 2 minutes (fat will rise to the top). Seal bag; carefully snip off bottom corner of bag. Drain drippings into measuring cup, stopping before fat layer reaches opening; discard fat.
Return vegetables to pan. Add wine mixture and broth to pan; cook 10 minutes over medium heat, scraping pan to loosen browned bits. Remove vegetables from pan using a slotted spoon; discard. Combine flour and water in a small bowl, stirring with a whisk to form a slurry; add slurry and 1/4 teaspoon salt to pan, stirring constantly. Simmer 1 minute or until slightly thick.
Remove skin from chicken; discard. Carve chicken, and serve with gravy.