Combine olive oil, balsamic vinegar, minced garlic, rosemary, thyme, paprika, salt, and pepper in a large bowl. Mix until the marinade is well blended, then add chicken pieces and toss thoroughly to coat every piece with the fragrant mixture.
Cover the bowl with plastic wrap and refrigerate for at least 15 minutes, though 30 minutes is ideal. The longer marinating time allows flavors to penetrate deeper into the chicken for maximum taste development.
While chicken marinates, prepare the honey-balsamic glaze by whisking together honey, Dijon mustard, and chicken broth in a small bowl. Set this mixture aside—it will become your finishing sauce on the grill.
Thread marinated chicken, bell pepper chunks, red onion, and mushrooms onto soaked wooden skewers in alternating pattern. This creates cozy labor day grilled chicken skewers with even cooking, as the variety of ingredients ensures nothing overcooks or undercooks.
Preheat grill to medium-high heat, approximately 400°F, and lightly oil the grates with vegetable oil. Grill skewers for 18-20 minutes, turning every 4-5 minutes to ensure even cooking and beautiful char marks on all sides.
During the final 5 minutes of cooking, brush the grilled chicken skewers generously with the honey-balsamic glaze. Watch carefully as the glaze caramelizes—this happens quickly and creates an irresistible golden coating.
Transfer finished skewers to a clean platter and let rest for 5 minutes before serving. This resting period allows juices to redistribute throughout the chicken for maximum tenderness and flavor.