In a medium bowl, combine the olive oil, garlic, balsamic vinegar, brown sugar, rosemary, and thyme. Season the mixture generously with salt and freshly ground black pepper. Whisk thoroughly to blend the flavors. Set aside 1/4 cup of this mixture in a smaller bowl for basting later. Cover and refrigerate until you're ready to use it.

Add the chicken breasts to the bowl with the remaining marinade, tossing them to coat evenly. Cover the bowl and let the chicken marinate for at least 20 minutes at room temperature, or refrigerate it for a more extended period, up to overnight, to deepen the flavors.

When you're ready to grill, preheat your grill (or grill pan) over medium-high heat for about 5 minutes. Grill the marinated chicken breasts, turning them halfway through, and basting with the reserved marinade to keep them juicy and flavorful. Cook until the internal temperature of the chicken reaches 165°F, which should take about 6 minutes per side.

Once cooked, transfer the chicken to a serving platter and sprinkle with freshly chopped parsley for a burst of color and freshness.