Start by cutting the chicken breasts into bite-sized pieces. Season with salt and black pepper.
In a mixing bowl, combine the soy sauce, oyster sauce, sugar, and additional black pepper. Set aside.
Heat the vegetable oil in a frying pan or wok over medium-high heat.
Add the chicken pieces to the pan. Stir-fry for about 5-7 minutes, or until the chicken is golden brown and cooked through. Remove the chicken from the pan and set aside.
In the same pan, add the sliced onions, garlic, and ginger. Sauté for 2 minutes until fragrant.
Add the sliced bell peppers and continue to stir-fry for another 2-3 minutes.
Return the cooked chicken to the pan and pour in the prepared sauce. Mix everything together and cook for an additional 2-3 minutes, allowing the flavors to meld.
Taste and adjust seasoning if necessary. Remove from heat.
Serve hot, garnished with chopped green onions.