Cut chicken in small, thin strips. Place the chicken and ½ cup sauce in a large plastic resealable bag. Marinate in refrigerator for at least 30 minutes. Remove chicken from bag and discard used sauce.
Prepare and measure the vegetables: Quarter baby carrots lengthwise. Cut red bell pepper into thin strips. Cut green onions into ¾ inch diagonal slices. Snow peas are whole.
Heat the oil in a large skillet or wok. Add the chicken and stir fry until no longer pink (about 4-6 minutes). Remove chicken and set aside.
Add 1 Tablespoon olive oil to the skillet and heat. Add carrots, snow peas, red bell pepper, and green onions and stir fry until tender-crisp (about 4-5 minutes). Add noodles and an additional ¼ cup Sesame Ginger Sauce. Cook and toss for 1 minute or until completely heated through. Sprinkle with toasted sesame seeds if desired.