Combine water, kosher salt, brown sugar, and apple cider vinegar in a large bowl. Stir until salt and brown sugar are dissolved. Place chicken breasts into brine, cover, and refrigerate for at least 4 hours or overnight.

Preheat an electric smoker according to manufacturer's directions to 225 degrees F (110 degrees C) using maple wood chips.

Remove chicken breasts from brine and rinse under cold water. Pat dry. Combine salt, black pepper, paprika, brown sugar, garlic powder, and onion powder in a bowl. Sprinkle dry rub all over chicken breasts and place skin-side up on a grill rack in the preheated smoker. Place a drip pan underneath.

Smoke chicken breasts in the preheated smoker until chicken is no longer pink at the bone and the juices run clear, about 4 hours, adding maple wood chips as necessary to keep the smoke continuous. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).