In a mixing bowl, whisk together the balsamic vinegar, extra virgin olive oil, low sodium chicken broth, minced garlic, honey, fresh rosemary, and Italian seasoning. Make sure all ingredients are well combined.
Place the boneless skinless chicken thighs in a large resealable bag or shallow dish. Pour the marinade over the chicken, ensuring it's well coated. Seal the bag or cover the dish and refrigerate for at least 30 minutes, or up to 4 hours for maximum flavor.
Heat a skillet over medium-high heat. Once hot, add the marinated chicken thighs, cooking for about 6-7 minutes per side, or until they reach an internal temperature of 165°F (74°C). Baste the chicken with the remaining marinade for extra flavor.
Once cooked, remove the chicken from the skillet and let it rest for a few minutes. This step is essential for keeping the chicken juicy. Slice the chicken, if desired, and serve it garnished with freshly chopped parsley.