In a medium bowl, whisk garlic, vinegar, oil, brown sugar, rosemary, and thyme; generously season with salt and pepper. Reserve ¼ cup marinade for grilling.
Add chicken to bowl and toss to combine. Cover bowl and refrigerate at least 20 minutes and up to overnight.
Prepare a grill for medium-high heat; preheat 5 minutes. Grill chicken, basting with reserved marinade and turning halfway through, until an instant-read thermometer inserted into thickest part registers 165°, about 6 minutes per side.
Transfer chicken to a platter. Top with parsley.
