To prepare teriyaki sauce, place soy sauce, water, vinegar, brown sugar, garlic, and cornstarch in a small saucepan over medium heat. Whisk gently until mixture begins to boil and thicken. Remove from heat and transfer to a bowl to cool.
Place chicken strips in a large Ziploc bag and coat with 1/2 cup teriyaki sauce. Marinate chicken tenders in the sauce for at least one hour or overnight in the refrigerator.
If using bamboo skewers, soak them in water for 30 minutes before cooking. Skewer chicken. Cook on prepared charcoal grill for 3-5 minutes on all sides until done. Brush strips with reserved teriyaki glaze for the last 1-2 minutes. Serves 4-6.