Boil the noodles according to package instructions. Drain in a colander in the sink and rinse under cold running water. Shake the colander to drain off excess water and pat the noodles dry with a towel.
Heat 1/4 cup of the peanut oil in a large seasoned or non-stick skillet over high heat. Add the noodles, spreading them out to evenly cover the skillet, and fry, turning once, until golden brown and crispy, about 8 minutes. (Break the noodles up, by stirring, near the end of the cooking). Transfer noodles to a paper towel-lined plate and season with salt to taste. Set aside. Discard any excess oil and wipe out the pan.
Whisk together the chicken broth, oyster sauce, soy sauce, cornstarch, and sugar in a small bowl, and set aside. Season the chicken with the dark sesame oil, salt, and pepper, and set aside.
Heat the skillet over high heat. Heat the remaining 2 tablespoons peanut oil until very hot. Add the ginger, garlic, and scallion and stir-fry, until fragrant, about 30 seconds. Add the chicken and stir-fry, until lightly browned, about 1 1/2 minutes. Add the onion, celery, and mushrooms and stir-fry, until crisp-tender, about 2 minutes. Add the water chestnuts and spread the ingredients to the outside of the pan to form a well in the center. Pour the chicken broth mixture into the well, bring to a boil, and stir to coat the chow mein mixture. Stir in the bean sprouts and remove from the heat. Season generously to taste with pepper.
Transfer chicken chow mein to a warm platter and top with the fried noodles. Serve immediately with rice. Pass more soy sauce at the table.
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