Cook sesame seeds in large nonstick skillet over medium heat until golden and fragrant; set aside.
In a large skillet, heat 2 teaspoons oil over medium-high heat. Add chicken; stir-fry 5 minutes until opaque in center; remove to a large plate.
Heat remaining oil in skillet. Add cabbage and peppers. Stir-fry 5 minutes until almost crisp-center.
Stir in remaining ingredients and chicken and heat through.
Sprinkle with sesame seeds and serve over white rice, if desired.