Cook the chow mein noodles according to package instructions, then drain and set aside.
In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the garlic and ginger, sautéing for about 30 seconds until fragrant.
Add the celery, carrots, and bell pepper to the skillet. Stir-fry for 3-4 minutes until the vegetables are tender-crisp.
Stir in the cooked chicken, bean sprouts, and green onions, cooking for an additional 2 minutes.
In a small bowl, whisk together the soy sauce, oyster sauce, cornstarch, chicken broth, and sesame oil until smooth.
Pour the sauce over the chicken and vegetables in the skillet. Stir well to coat everything evenly and cook for another 2-3 minutes until the sauce thickens.
Add the cooked chow mein noodles to the skillet, tossing everything together until the noodles are heated through. Season with salt and pepper to taste.
Serve hot, garnished with additional green onions if desired.