In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the sliced chicken and cook for about 5-7 minutes, or until browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the red and yellow bell peppers, broccoli, and snap peas. Stir-fry the vegetables for about 3-4 minutes until they are tender-crisp.
Add the minced garlic and ginger to the skillet, cooking for an additional 1-2 minutes until fragrant.
In a small bowl, whisk together the soy sauce, honey, cornstarch, and water until smooth. Pour this mixture into the skillet with the vegetables.
Return the cooked chicken to the skillet and stir everything together, cooking for another 2-3 minutes until the sauce thickens and coats the chicken and vegetables.
Drizzle with sesame oil before serving. Serve hot over cooked rice or noodles.