Heat vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken pieces and cook until browned, about 5-7 minutes.
Remove the chicken from the pan and set aside.
In the same pan, add garlic and ginger, stirring for 30 seconds.
Add mixed bell peppers and snap peas; stir-fry for 3-4 minutes.
Return the chicken to the pan.
Pour in the soy sauce and oyster sauce; toss to coat all ingredients.
Drizzle with sesame oil and stir-fry for another 2 minutes.
Check for seasoning and adjust if necessary.
Serve hot over cooked rice.