Cut chicken into 1/4-inch-thick strips; cut onion in half, and cut halves into slices. Cut bell peppers into 1/4-inch-thick strips, and cut carrots and green onions diagonally into slices. Set aside.
Whisk together broth and next 5 ingredients until smooth.
Heat sesame oil in a wok or large skillet at medium-high heat 2 minutes. Add chicken, and stir-fry 3 to 5 minutes or until lightly browned. Add vegetables, and stir-fry 3 to 4 minutes. Add broth mixture, and stir-fry 1 minute or until thickened. Serve over rice. Garnish, if desired.