Pound chicken breasts to 1-inch thick and cut into 4-ounce portions.
In a medium-sized bowl whisk together vinegar, broth, honey, garlic, salt, pepper, and rosemary. Reserve ½ cup of marinade and add remaining ~¼ cup to a 1-gallon ziplock bag with the chicken breasts.
Marinate for 15-30 minutes.
In a large cast-iron skillet over medium-high heat add oil and chicken, letting excess marinade drip off of it before adding to the skillet. Cook for 3-4 minutes per side, or until it is cooked through and internal temperature reaches 165 degrees. (Check with a meat thermometer.)
Meanwhile, in a separate, small saucepan or skillet add remaining balsamic marinade and bring to a boil. Boil for 1 minute and then reduce heat to simmer.
Let balsamic vinegar mixture simmer for 10 minutes or until it is reduced by half and forms a glaze.
Serve cooked chicken breasts with balsamic glaze and enjoy!
