In a bowl, combine the soy sauce, oyster sauce, and cornstarch. Add the chicken pieces and mix well. Let the chicken marinate for 15-20 minutes.
Heat vegetable oil in a large skillet or wok over medium-high heat. Add the crushed black peppercorns and stir-fry for about 30 seconds to release their aroma.
Add the minced garlic and grated ginger to the skillet and stir-fry for another 30 seconds, until fragrant.
Add the marinated chicken to the skillet and spread it out into an even layer. Let it cook undisturbed for 2-3 minutes to sear and develop a golden brown crust.
Stir in the sliced onion and bell pepper, and continue to cook for another 3-4 minutes, or until the vegetables are tender-crisp and the chicken is cooked through.
Garnish with chopped green onions and serve the Black Pepper Chicken hot over cooked rice.