Place 3-5 wooden skewers in a shallow plate or pan filled with water. Let them soak for 30 minutes to prevent them from burning on the grill.
Trim any excess fat from the chicken breasts and cut them into 1-inch chunks. In a medium mixing bowl, whisk together the balsamic vinegar, extra-virgin olive oil, minced garlic, 1 tablespoon honey, 1 teaspoon minced fresh rosemary, kosher salt, and freshly ground black pepper. Add the chicken chunks to the marinade, stir to coat well, cover, and refrigerate for 1-2 hours. Marinating allows the chicken to absorb great flavor—I always let it go the full 2 hours for extra tenderness.
Preheat your grill to high heat. Remove the soaked skewers from water and thread the marinated chicken chunks (from Step 2) onto the skewers, spacing the pieces slightly apart so they cook evenly.
Lightly oil the grill grates using non-stick cooking spray or by brushing them with olive oil. Reduce the heat to medium-high. Place the threaded chicken skewers on the grill and cook for 3-5 minutes per side, turning occasionally. Baste the chicken with the 2 tablespoons of honey during grilling. Grill until the chicken is opaque and cooked through, about 10 minutes total.
Transfer the grilled chicken skewers to a plate and let them rest for 2-3 minutes before serving. Drizzle with additional honey if desired and garnish with extra fresh rosemary. I like to sprinkle a touch of fresh rosemary for a burst of herbal aroma right before serving.