Heat the vegetable oil in a large skillet or wok 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 minced garlic and sauté for about 30 seconds until fragrant.
Add the broccoli, bell pepper, and snap peas to the skillet. Stir-fry the vegetables for about 3-4 minutes until they are tender-crisp.
In a small bowl, mix together the soy sauce, honey, rice vinegar, and sesame oil. Pour this sauce over the vegetables in the skillet.
Return the cooked chicken to the skillet and stir to combine. Add the cornstarch mixture to thicken the sauce, stirring constantly for about 1-2 minutes until the sauce is glossy and thickened.
Remove from heat and garnish with sliced green onions. Serve hot over cooked rice or noodles.