In a large plastic zip-top bag, combine the brown sugar, salt, garlic powder, paprika, onion powder, pepper, and olive oil. Add the chicken and massage until the chicken is thoroughly coated. Let marinate at room temperature for 10-15 minutes or refrigerated for up to 12 hours.
Preheat the grill on medium-high.
Remove the chicken from the marinade. Place the chicken on the grill and cook until the chicken begins to lightly char, about 4-6 minutes per side. Continue cooking, turning occasionally, until the internal temperature of the chicken reads 165°F on an instant-read thermometer, about 10 minutes more. Transfer to a cutting board and let rest for at least 5 minutes.