Step 1

Cut chicken into bite-size strips. In a medium bowl combine 2 tablespoons of the soy sauce, the rice vinegar, and 2 teaspoons of the sugar. Add chicken; toss to coat. Let stand at room temperature for 20 minutes or cover and chill for 1 hour. Cook noodles according to package directions until tender; drain. Rinse with cold water; drain well. Set noodles aside. For sauce, in a small bowl stir together chicken broth, the remaining 4 tablespoons soy sauce, the remaining 2 teaspoons sugar, and the cornstarch. Set aside.

Step 2

Pour vegetable oil and sesame oil into a wok or large nonstick skillet. Heat over medium-high heat. Add garlic; cook and stir for 30 seconds. Add carrot; cook and stir for 2 minutes. Add bok choy and green onion; cook and stir for 2 minutes more. Remove vegetables from wok.

Step 3

Drain chicken; discard marinade. Add chicken to wok (add more oil, if necessary); cook and stir for 3 to 4 minutes or until no longer pink. Push chicken from center of wok. Stir sauce and add to center of wok. Cook and stir until thickened and bubbly. Add the cooked noodles and vegetables. Using two spatulas or wooden spoons, lightly toss the mixture until combined and heated through. Transfer to a serving platter. If desired, sprinkle with sesame seeds. Serve immediately.