Cut each chicken breast in half. Blot the chicken dry with a paper towel.
Heat a large skillet over medium-high heat. Add the butter and olive oil. When the butter has melted, add the whole garlic cloves and cook for about 30 seconds to flavor the butter. Once the garlic is golden, discard.
Add the chicken breasts and cook until well-browned on both sides, about 1-2 minutes.
Reduce the heat to medium and add the vinegar and salt. Cover and cook for about 5 minutes until the vinegar aroma subsides.
Add the rosemary and vermouth. Cook uncovered until the chicken is tender and has reached 165 degrees Fahrenheit on a thermometer (about 10 minutes). Remove the chicken to a large platter.
Add the peppercorns to the skillet and bring the sauce to a boil. Boil for 3 – 5 minutes until the sauce has reduced and is slightly thickened. Pour over the chicken to serve.
This recipe is for 6 servings. Each serving is half of a chicken breast.You can replace the butter with olive oil, but keep in mind that the butter adds body to the sauce.You can substitute the dry vermouth with white wine, or use chicken stock to omit the alcohol entirely.Chicken can be stored in an airtight container in the refrigerator for 3-4 days or in the freezer for several months.