Heat 2 tablespoons vegetable oil in a wok or large skillet over high heat. Add chicken to the wok, and stir-fry until chicken is opaque on all sides, about 3 minutes. Remove to a plate.

Heat the remaining 1 tablespoon vegetable oil in the wok. Add bell pepper, onion, and snow peas; stir-fry until vegetables start to soften, 3 to 4 minutes. Reduce heat to medium-low.

Whisk together water, hoisin sauce, soy sauce, sherry, ginger, rice vinegar, sesame oil, oyster sauce, sugar, cornstarch, and garlic in a bowl. Add sauce to the wok, stirring constantly until sauce starts to thicken. Add chicken back to the wok, stir, and reheat, 1 to 2 minutes.