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Step 1
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.
Step 2
Preheat an electric smoker according to manufacturer's directions to 225 degrees F (110 degrees C) using maple wood chips.
Step 3
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.
Step 4
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).