In a medium bowl, combine the chicken pieces, soy sauce, and cornstarch. Mix well and let marinate for 15-20 minutes.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and stir-fry until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced onion, garlic, and ginger. Stir-fry for 2-3 minutes until fragrant and the onion is translucent.
Add the bell pepper and black pepper to the skillet, cooking for another 2-3 minutes until the pepper is tender.
Return the chicken to the skillet and add the oyster sauce, rice vinegar, and sugar. Stir well to combine and heat through for another 2 minutes.
Serve hot, garnished with chopped green onions.