In a bowl, combine chicken, soy sauce, and cornstarch. Let it marinate for 10 minutes.
Heat vegetable oil in a large skillet over medium-high heat.
Add chicken and cook until browned and fully cooked, about 5-7 minutes. Remove from the skillet.
In the same skillet, add bell peppers, broccoli, garlic, and ginger. Stir-fry for 3-4 minutes until tender-crisp.
Return chicken to the skillet. Add oyster sauce, hoisin sauce, and sesame oil.
Toss everything together and cook for another 2 minutes.
Serve hot over cooked rice.