Heat the olive oil over medium-high heat in a large pot.
Add the chicken to the pot and cook the chicken for 10 minutes, stirring occasionally.
Once the chicken has cooked, add the bok choy, snow peas, carrots, celery, onion, garlic, and ginger. Sauté over medium heat for 3 minutes.
Add the chicken broth, peanut butter, soy sauce, sesame oil, rice vinegar, and red pepper.
Stir together, cover the pot, turn the heat to high, and bring the pot to a boil. It should take about 10 minutes to come to a boil. Make sure to stir the soup every few minutes to prevent it from sticking to the bottom of the pot.
Once the soup is boiling, remove the cover, reduce the heat to medium, and add the rice noodles. Cook the rice noodles for half the recommended time on the package.
Remove the pot from the heat and let the soup sit uncovered for 5 minutes. The noodles will continue to cook as the soup cools.