1. To make brine for soaking the chicken, combine the salt, sugar and water in a large nonmetallic bowl. Stir to completely dissolve the salt and sugar.
2. Place the chicken thighs in the brine, making sure all the pieces are submerged. Cover the bowl with plastic wrap and refrigerate for 1 hour.
3. Meanwhile, to make spice rub, mix together brown sugar, paprika, cumin, cayenne pepper, black pepper, garlic powder and onion powder in a small bowl.
4. Lightly brush the grill rack with vegetable oil. Then prepare the grill with low-heat coals or heat a gas grill.
5. Remove the chicken from the brine and pat dry. Dust chicken on both sides with the spice rub, pressing gently to make sure the rub adheres; if keeping the skin on, spread the rub evenly under the skin with your fingers.
6. Grill chicken, uncovered, for about 5 minutes per side, until the surfaces begin to brown. Turn the thighs over, cover the grill and cook for 5 more minutes per side. Uncover and continue grilling, turning the thighs every 5 minutes, until an instant-read thermometer inserted in thickest part of a thigh, without touching a bone, registers 170 degrees F, about 10 to 15 minutes more; surfaces should be mahogany brown and flesh should feel firm.