Brining the chicken makes the meat tender and melt in your mouth. These barbecued chicken sliders are best served with extra napkins.
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In a large bowl, mix brine ingredients, stirring to dissolve brown sugar. Reserve 1 cup brine for cooking chicken; cover and refrigerate.
Place chicken in a large resealable bag; add remaining brine. Seal bag, pressing out as much air as possible; turn to coat chicken. Place in a large bowl; refrigerate 18-24 hours, turning occasionally.
Remove chicken from brine and transfer to a 3-quart slow cooker; discard brine in bag. Add reserved 1 cup brine and 1/3 cup liquid smoke to chicken. Cook, covered, on low 4-5 hours or until chicken is tender.
Remove chicken; cool slightly. Discard cooking juices. Shred chicken with two forks and return to slow cooker. Stir in barbecue sauce; heat through. Serve on buns.