Preheat the oven to 350F and lay four 12×12 inch squares of foil on your work surface.
While the oven is preheating, whisk together 1 tbsp corn starch and 2 tbsp water. Set aside. Whisk together the remaining sauce ingredients in a small saucepan.
Bring the mixture to a boil, then pour in water and corn starch mixture. Whisk until the sauce begins to thicken. Set aside and allow to thicken and cool while you prepare the foil packets.
Place cubed chicken, peppers, onions, broccoli, snap peas, and 1 cup of sauce in a bowl. Toss to evenly coat.
Distribute the chicken and vegetable mixture evenly between the sheets of foil and fold the foil over the chicken and vegetables to close off the pack. Pinch the ends together so the pack stays closed.
For Oven: Transfer the chicken foil packs to a baking sheet and bake for 25 minutes or until chicken is cooked through and veggies are tender.
If cooking on the grill: Preheat the grill to medium-high heat. Place foil packets on grill and grill for 6-7 minutes, then flip over and grill for an additional ~5 minutes (depending on the thickness of the chicken) or until chicken is cooked through.
When chicken is done, carefully open the foil packs, drizzle with more sauce as desired, serve immediately and enjoy!