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 until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the garlic and ginger, sautéing for about 30 seconds until fragrant.
Add the sliced bell peppers, broccoli, and snap peas to the skillet. Stir-fry for 3-4 minutes until the vegetables are tender-crisp.
Return the cooked chicken to the skillet. In a small bowl, mix the soy sauce, honey, rice vinegar, and cornstarch mixture. Pour this sauce over the chicken and vegetables. Stir well to combine and cook for an additional 2-3 minutes until the sauce thickens.
Serve the stir-fry over cooked rice or noodles.