In a pot of salted boiling water, cook the noodles according to the directions on the package. Drain well.
In a nonstick pan on medium-high heat, heat both oils. Add in the peppers, onions, mushrooms, and celery. Sauté for 4 - 5 minutes. Add in the chicken, garlic, and ginger and cook until the chicken is no longer pink and has a nice golden brown. Add the chicken broth and soy sauce; bring to a low simmer for about 6 minutes.
Add the snow peas and cook for about 2 minutes. Toss in the noodles and serve.