In a medium bowl, combine the chicken pieces with soy sauce and cornstarch. Mix well and let marinate for at least 15 minutes.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and ginger. Sauté for about 30 seconds until fragrant.
Add the sliced bell pepper and onion to the skillet. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Return the cooked 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 until everything is heated through.
Serve hot, garnished with chopped green onions.