Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the chicken pieces and season with salt and pepper. Cook for about 5-7 minutes, stirring frequently, until the chicken is browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the bell peppers, broccoli, and snap peas. Stir-fry the vegetables for about 4-5 minutes until they are tender-crisp.
Add the minced garlic and ginger to the skillet, stirring for about 30 seconds until fragrant.
In a small bowl, whisk together the soy sauce, honey, sesame oil, cornstarch, and water. Pour this sauce over the vegetables in the skillet and stir well to combine.
Return the cooked chicken to the skillet and toss everything together until the chicken is heated through and the sauce thickens slightly, about 2-3 minutes.
Serve the stir fry over cooked rice or noodles.