1. Rinse chicken thighs under cold water and pat dry with paper towels.
2. Heat a large skillet over medium high heat. Add olive oil and butter. Lightly season chicken thighs with salt and add to the skillet (when it's very hot).
3. Cook on first side for about 10 minutes, then turn on the other side. Cook another 8-10 minutes.
4. Remove chicken from the skillet and set aside. Add garlic to the skillet and cook for about 40 seconds, stirring with a spatula.
5. Add chicken broth and stir. Add balsamic vinegar, then add heavy cream. Bring the sauce to a gentle simmer.
6. Return chicken to the skillet and cook for about 8 minutes, until it's cooked through and the sauce thickened.
7. Sprinkle with chopped parsley. Serve over rice, pasta or mashed potatoes.