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 broccoli, red bell pepper, and snap peas. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Add the minced garlic and grated ginger to the skillet, stirring for about 30 seconds until fragrant.
In a small bowl, whisk together the peanut butter, soy sauce, honey, rice vinegar, and sesame oil until smooth.
Return the cooked chicken to the skillet and pour the peanut sauce over the chicken and vegetables. Stir well to coat everything evenly and heat through for another 2-3 minutes.
Serve the stir-fry over cooked rice or noodles, garnished with chopped green onions and sesame seeds if desired.