Trim any fat from the chicken and place chicken in a large saucepan. Add enough water to cover chicken by 2 inches. Bring to a slow simmer, then reduce heat slightly so that water remains still. Cook 20-25 minutes until the internal temperature reaches 165*F and chicken is no longer pink. Remove chicken from cooking liquid, cool slightly, then cut into large cubes. Discard cooking liquid.
Heat another large saucepan over moderate heat. Add oil and swirl to coat bottom of pan. Once oil is hot, add carrots and celery and stir for 2 minutes.
Add stock to the saucepan. Bring to a simmer and add noodles. Cook 2-3 minutes. Add scallions, Napa cabbage, edamame and white pepper. Continue to simmer for an additional 2-3 minutes.