In a large bowl, combine chicken cubes with 3/4 cup of the teriyaki marinade, plus salt and pepper to taste. Toss to coat well. Cover and refrigerate for at least 30 minutes (up to 4 hours).
If using wooden skewers, soak them in water for 30 minutes ahead of time to prevent burning.
Get the grill going; the temperature should be at least 375 degrees. (Lightly oil the grates if needed.)
Slide the chicken and veggies onto each skewer. You will alternate between vegetables, then add a piece of the chicken breasts.
Repeat the addition of marinated chicken or mushroom, red onion, zucchini, and pineapple.
Place skewers on the preheated grill and cook for 15 to 20 minutes, turning once after about 7 minutes.
Brush each skewer with the remaining marinade (about a 1/4 cup) or a Hawaiian barbecue sauce.
Transfer kabobs to a plate.
Serve hot.