In a bowl, whisk together balsamic vinegar, olive oil, brown sugar, garlic, and dried herbs, and season liberally with salt and pepper. Reserve ¼ cup of the marinade.
Add chicken to the bowl and toss to combine. Let marinate at least 20 minutes and up to 12 hours.
Preheat grill over medium high. Add chicken and grill, brushing with reserved marinade, until cooked through, 6 minutes per side.