Pound the chicken breasts down to 1-inch thick. This ensures they cook evenly.
Place the chicken breasts, balsamic vinegar, honey, Italian seasoning or oregano, and garlic cloves in a zip bag. Marinate the chicken for 20 to 30 minutes. This can be marinated overnight.
Grill:
Preheat the grill to medium-high heat (around 375F in the gauge). Grease the grills and place the chicken breasts on the hot grates. Grill for 7 minutes on the first side, flip, and cook the other side for 5-7 minutes, until the internal temperature reaches 165F.