In a small bowl, stir together cornstarch, sugar, soy sauce, and toasted sesame oil. Place cubed chicken in a disposable plastic bag and pour mixture over the top. Toss to coat. Allow to marinate for at least 15 minutes, up to 12 hours.
In a medium wok or saute pan (with a lid), heat oil over medium high heat. Once hot, add chicken and cook until cooked through. Transfer chicken to a plate and tent with foil to keep warm.
Return pan to heat. Deglaze with a couple tablespoons of the water and add onion and garlic. Cook for three minutes, until onion just begins to turn translucent around the edges.
Add green beans and bell pepper and cook for another three minutes. Add 2 tablespoons of the water, cover, and continue to cook until vegetables reach your desired level of doneness, adding more water as necessary, about 3 to 8 minutes*.
Stir in chicken and cook just until chicken is hot. Salt to taste.
Serve over white rice.