1. Preheat the oven to 350°F.
2. Sprinkle the chicken parts with the salt, pepper and thyme. Heat the oil in a large skillet set over medium-high heat. In batches, brown the chicken on all sides, about 15 minutes total. Transfer the chicken to a roasting pan as the pieces have browned. The roasting pan should be big enough that the chicken pieces fit snugly together and no larger.
3. Drain all but 2 tablespoons of oil from the skillet. Add the celery root chunks. Cook, stirring, until the pieces are nicely browned, about five minutes. Transfer the celery root to the roasting pan. Stir the garlic cloves into the pan, adding some of reserved oil if necessary to prevent the pan from overbrowning or the garlic from sticking to the pan. Cook about five minutes, and then transfer the garlic to the roasting pan.
4. Pour the wine into the pan, scraping the brown bits from the bottom of the pan with a wooden spoon. Pour in the stock. Bring the mixture to a boil.
5. Transfer the chicken to a serving platter and tent with foil. Place the roasting pan on top of an element over high heat. Bring the mixture to a boil. Boil gently until the mixture has reduced and thickened very slightly. Pour the juices and the vegetables over the chicken pieces.
6. Pour the wine mixture over the chicken, celery root and garlic in the roasting pan. Cover the pan with aluminum foil and roast in the center of the preheated oven, stirring once or twice, until the juices run clear when the thighs are poked with a fork, about 30 minutes.