In a small bowl, whisk together soy sauce, oyster sauce, sesame oil, cornstarch, and chicken broth, then set aside.
Heat 2 tablespoons vegetable oil in a large wok or skillet over high heat, add the chicken, and cook for 5-6 minutes until golden and cooked through, then remove to a plate.
Add remaining 1 tablespoon oil to the pan, then add bell pepper, snap peas, and carrots, stir-frying for 3-4 minutes until crisp-tender.
Add garlic and cook for 30 seconds until fragrant, then return chicken to the pan.
Pour the sauce over everything and stir constantly for 1-2 minutes until the sauce thickens and coats the chicken and vegetables, then serve immediately over rice or noodles.