In a large skillet, heat the oil. Brown the chicken over medium high heat for 10 minutes; turn and brown for 10 minutes more. Cover the pan and continue cooking over low heat for 20 to 25 minutes, until the chicken is done.
Meanwhile, finely grind the garlic and walnuts.
When the chicken is tender, transfer it to a plate and keep warm. Pour off all but 4 tablespoons of the pan drippings. Add the ground garlic and nuts mixture, water and the parsley to the pan. Add about 1/4 teaspoon of salt and simmer the sauce on medium heat for approximately 5 minutes. Place the chicken pieces back in the pan, turning them to coat them with the sauce. Heat thoroughly before serving.