Preheat the oven to 350°F (180°C) and line a baking sheet with parchment paper.
Pat the chicken leg quarters dry with paper towels to remove excess moisture.
In a mixing bowl combine brown sugar, paprika, salt, dried thyme, garlic powder, onion powder, and black pepper.
Pour the olive oil over the spice mixture and stir until it forms a uniform paste.
Place the chicken on the prepared baking sheet and rub the oil-spice mixture evenly over all surfaces of each piece.
Bake in the preheated oven for 40 minutes, or until the chicken reaches an internal temperature of 175°F (79°C).
Remove the chicken from the oven and let it rest for 10 minutes before serving.
