Cut the chicken breasts into slivers (1 inch by 1/4 inch).
Stir together soy sauce, wine, vinegar, ginger and garlic. Add the chicken pieces, mix so the chicken is coated with the marinade and let stand for at least 15 minutes.
Add oil to wok over high heat. When oil is hot, add the walnut pieces. Toss until the color changes, less than a minute. Set aside.
Add the scallions to the rest of the oil and fry briefly until the color brightens. Set aside.
Add the chicken to the pan, reserving the marinade. Stir-fry until opaque, 1-2 minutes.
Add the stock and the reserved marinade and bring the mixture to a boil. Stir the cornstarch in the water so it is evenly dissolved and add it to the mix along with the scallions. Cook and stir until the sauce is thickened.