Place chicken in a resealable plastic bag, pour 1/4 cup of Alabama White BBQ Sauce over the top. Shake to coat. Seal and refrigerate for 6 - 8 hours or overnight.
Heat grill for indirect heat. Place 1/4 cup of BBQ sauce in a bowl next to the grill. Cook chicken for 7 minutes.Turn chicken and cook for 5 - 7 more minutes or until chicken is cooked through. Transfer to a plate and let rest for 5 minutes.
Shred chicken.
To assemble the sandwiches place chicken on bottom buns, drizzle with remaining BBQ sauce and top with 3 - 4 bread and butter pickles. Serve.