Place the balsamic vinegar, honey, olive oil and rosemary in a large zip lock bag. Add the chicken, seal the bag and refrigerate, turning occasionally, for at least 2 hours or overnight.
Preheat the oven to 350°F.
Remove the chicken from the marinade, discarding the marinade. Season the chicken with salt and freshly ground black pepper.
Heat a large ungreased cast-iron skillet or a large heavy skillet over medium high heat. Cook the chicken for 3 to 4 minutes per side or until nicely browned on both sides. Transfer the skillet to the oven and bake for 20 minutes or until the juices run clear when pierced with a fork.