In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the chicken pieces and 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 broccoli, bell pepper, and snap peas. Stir-fry the vegetables for about 3-4 minutes until they are tender-crisp.
Add the minced garlic to the vegetables and stir-fry for an additional 30 seconds until fragrant.
In a small bowl, whisk together the honey, soy sauce, cornstarch, water, and sesame oil until smooth.
Return the cooked chicken to the skillet with the vegetables. Pour the honey garlic sauce over the chicken and vegetables, stirring to coat everything evenly. Cook for another 2-3 minutes until the sauce thickens and bubbles.
Serve the honey garlic chicken stir-fry over cooked rice or noodles.