In a large bowl, whisk together oil, honey, tamari sauce, mustard, rice vinegar, garlic, pepper, and thyme.
Add chicken, bell peppers, onions, zucchini, and mushrooms. Toss to coat and refrigerate for up to 24 hours.
Preheat the grill to high heat.
Thread chicken and vegetables alternately onto skewers.
Lightly oil the grill. Place skewers on grill and cook, turning frequently for about 15-20 minutes, until chicken is cooked through and vegetables are tender. Serve.