In a medium bowl, whisk olive oil, brown sugar, garlic, thyme, and rosemary to blend. Generously season mixture with salt and pepper, and whisk to combine. Reserve 1⁄4 cup of the marinade for basting.
Add chicken thighs to bowl, toss to coat, and place in refrigerator to marinate for at least 20 minutes, and up to overnight.
Preheat a wood-, charcoal-, or gas-burning grill to medium-high.
Place the chicken on the grill, meat side down first, and cook for about 6 minutes per side, basting with the reserved marinade, until cooked through and the juices run clear.
Garnish with parsley before serving.