Preheat your grill: light the gas grill or heat charcoal until medium-low heat is reached.
In a medium bowl, whisk together balsamic vinegar, Dijon mustard, brown sugar, salt, minced garlic, and black pepper until smooth.
Add the chicken thighs to the bowl (or place both marinade and chicken in a gallon resealable bag) and turn to coat all pieces thoroughly, ensuring marinade gets into any crevices.
Marinate the chicken for at least 30 minutes or up to overnight in the refrigerator.
Place the marinated thighs on the preheated grill over medium-low heat and cook for about 8 minutes total; turn once around the 6-minute mark so they finish cooking evenly.
Remove the chicken when cooked through, let rest for 5 minutes, then serve over a bed of fresh salad greens or prepared salad.