Place cubed chicken into a large zip lock baggie with 1 cup teriyaki sauce. Allow to marinate for at least one hour or as long as overnight.
Prep all veggies.
If you are using wooden skewers, make sure to soak them in cold water prior to skewering. This prevents them from burning on the grill.
Skewer meat and veggies in any order you'd like.
BBQ on medium grill, turning often until veggies are tender and chicken reaches a safe cooking temp of 160*
Measure teriyaki sauce into a small saucepan, stir in brown sugar. Heat over medium heat until it comes to a low boil.
Stir ¼ cornstarch into about a tablespoon of water until well blended. Stir into teriyaki sauce. Reduce heat to low and continue to simmer until sauce begins to thicken (20-30 minutes).
Serve over a bed of white rice and top with a drizzle of teriyaki glaze, and chopped green onion.