In a medium bowl, combine the balsamic vinegar, extra virgin olive oil, low sodium chicken broth, minced garlic, honey, minced rosemary, and Italian seasoning. Whisk together until well blended.
Place the chicken thighs in a large resealable plastic bag or a shallow dish. Pour the marinade over the chicken, ensuring each piece is well-coated. Seal the bag or cover the dish and refrigerate for at least 30 minutes, or up to 4 hours for maximum flavor.
Remove the chicken from the marinade, reserving the marinade for later use. Heat a large skillet over medium-high heat and add a splash of olive oil.
Once the skillet is hot, add the chicken thighs in a single layer. Sear them for about 5-6 minutes on each side, or until they are golden brown and cooked through (internal temperature should reach 165°F).
After the chicken is cooked, remove it from the skillet and set aside. Pour the reserved marinade into the skillet, scraping up any brown bits from the bottom. Bring to a simmer and let it cook for about 5-7 minutes, or until it thickens slightly.
Return the chicken to the skillet, coating it in the balsamic sauce. Cook for an additional 1-2 minutes until the chicken is heated through. Serve hot, garnished with chopped parsley for a fresh touch.