In a mixing bowl, combine the chicken pieces, soy sauce, oyster sauce, cornstarch, and black pepper. Mix well and let marinate for about 10 minutes.
Heat the vegetable oil in a wok or large frying pan over medium-high heat.
Add the marinated chicken to the pan and stir-fry for about 5-7 minutes until the chicken is cooked through and slightly browned. Remove the chicken from the pan and set aside.
In the same pan, add the sliced onion, bell pepper, garlic, and ginger. Stir-fry for about 3-4 minutes until the vegetables are tender but still crisp.
Return the cooked chicken to the pan, and add water. Stir to combine and cook for an additional 3-4 minutes, allowing the flavors to meld.
Taste and adjust seasoning with salt and additional black pepper if needed.
Serve hot, garnished with sliced green onions if desired, and enjoy with steamed rice or noodles.