In a medium bowl, combine the chicken pieces, 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 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 and bell pepper. Stir-fry for about 3-4 minutes until they start to soften.
Add the minced garlic and ginger to the skillet and stir-fry for an additional 1-2 minutes until fragrant.
Return the cooked chicken to the skillet. Add black pepper, oyster sauce, rice vinegar, and sugar. Stir well to combine and cook for another 2-3 minutes to heat through.
Serve hot, garnished with chopped green onions.