Place chicken in the bottom of a slow cooker. In a bowl, combine brown sugar, soy sauce, vinegar, garlic, ginger and pepper. Pour over chicken in slow cooker and cover; cook on low 6-8 hours or until chicken is tender.
Remove chicken from the slow cooker and set aside. Whisk together cornstarch and water in a small bowl; pour into the sauce remaining in the slow cooker and whisk well. Turn the slow cooker heat up to high, cover, and allow to thicken for about 20 minutes.
Meanwhile, shred chicken. Once sauce has thickened, return chicken to the crock pot and toss with sauce; allow to heat through for 2-3 minutes and serve hot.