In a large pot, bring 4 quarts of water to boil. Add noodles to boiling water and cook until tender, 2-4 minutes. Drain and rinse noodles with cold water, and then drain again. In a medium bowl add noodles and toss with sesame oil; set aside.
In another bowl dissolve the baking soda and ½ cup cold water. Add chicken and let sit for 15 minutes. Drain and rinse chicken with cold water, and then drain again.
Use paper towels to pat chicken dry. In the now empty bowl, combine 1 tablespoon rice wine, 2 teaspoons cornstarch, and chicken; set aside.
In another bowl whisk together broth, soy sauce, oyster sauce, pepper, remaining 2 tablespoons rice wine, and remaining 1 teaspoon cornstarch; set aside.
Heat oil in a 12-inch nonstick skillet over medium high heat until the oil just begins to smoke. Add chicken and cook, stirring often, until opaque, about 2-3 minutes. Add carrots and celery and cook until tender but still crisp, about 1 minute. Finally, add scallion whites, garlic, and ginger and cook until fragrant, about 30-60 seconds.
Give broth mixture a quick whisk to recombine, and then add to skillet and cook until thickened and chicken is cooked through about 2 minutes.
Stir in bean sprouts and noodles and toss to combine and evenly coat everything in sauce, about 1 minute. Transfer chicken chow mein to a platter, sprinkle with scallion greens and serve.