Combine sauce ingredients in a small saucepan and heat over low heat, stirring until combined. Keep warm.
Cook the noodles according to the package directions.
Season the chicken with salt and pepper. Heat 1 tablespoon oil in a large skillet over medium-high heat. Cook the chicken for 5-7 minutes or until cooked through. Remove from the skillet. Add the last tablespoon of oil, then add the carrots and peppers. Cook for 3-4 minutes or until crisp tender.
Add the chicken back to the pan along with the noodles and sauce. Cook until warmed through. Garnish with green onions and serve.