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.
Cook:
Heat a large pan over medium-high heat. Once hot, add the oil. Remove the chicken breasts from the marinade and cook the first side for 7 minutes, flip them over, and cook them for another 5 minutes, until the internal temperature reaches 165F. Cook them in batches if necessary, moving them off the pan onto a covered plate.
Make the sauce:
Once the chicken breasts are cooked and out of the pan, add the chicken broth and the marinade from the bag into the pan. Bring it to a simmer, while scraping the tidbits left from the chicken in the pan, cooking it for 5 minutes to reduce the sauce. Turn off the heat.
Serve:
Serve the cooked balsamic chicken breasts with the sauce.