Put the chicken into a medium saucepan, and add enough water to cover completely. Bring the water to a boil, and then turn the heat down to medium. Gently parboil the chicken for 10 minutes, skimming off any scum that forms on top of the liquid. Drain the chicken and discard the water.
Transfer the chicken to a medium clay pot or a medium Dutch oven. Add the chestnuts, shiitake mushrooms and the ginger to the pot and distribute them evenly among the chicken pieces. Add the Shaoxing cooking wine, soy sauce, sugar and ground white pepper to the pot. Add enough water to cover all the ingredients. Bring the liquid to a boil over high heat then turn the heat down to low and slowly simmer the ingredients. Cook for about 30 minutes or until the chicken is tender.
Serve the braise hot in the clay pot.