For the Brine, pour cold water, apple cider and syrup into large plastic or glass container, or 2-gallon resealable plastic bag. Stir in salt until dissolved. Place chicken in brine to cover. If necessary, place a plate on top of chicken breasts to keep them submerged. Cover container or seal bag.
Refrigerate at least 2 hours. Remove chicken from brine. Discard remaining brine. Rinse chicken under cool running water. Pat dry. Brush chicken lightly with oil. Rub with Seasoning.
Grill over medium heat 6 to 8 minutes per side or until chicken is cooked through.