Slice the chicken breasts into thin strips if they are not already sliced. Slice the bell peppers and onion, cut the broccoli into small florets, and mince the garlic and ginger.
Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the minced garlic and minced ginger. Stir for about 30 seconds until fragrant.
Add the sliced chicken to the pan. Cook for 5–7 minutes, stirring often, until the chicken is fully cooked and no longer pink.
Add the sliced red bell pepper, sliced green bell pepper, broccoli florets, and sliced onion. Stir everything together and cook for 3–4 minutes until the vegetables are slightly tender but still crisp.
Pour in the sweet chili sauce, soy sauce, and oyster sauce. Stir well so the chicken and vegetables are evenly coated with the sauce.
Season with salt and black pepper to taste. Mix everything well.
Cook for another 2–3 minutes, stirring occasionally, until everything is hot and the sauce lightly coats the chicken and vegetables.