In a medium bowl, combine chicken pieces, soy sauce, and cornstarch. Mix well and let marinate for at least 15 minutes.
Heat 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 chicken from the skillet and set aside.
In the same skillet, add onion, garlic, and ginger. Stir-fry for 2-3 minutes until fragrant.
Add bell pepper and continue to stir-fry for another 2 minutes.
Return the chicken to the skillet. Add black pepper, oyster sauce, rice vinegar, and sugar. Stir well to combine and cook for an additional 2-3 minutes.
Remove from heat and garnish with chopped green onions before serving.