Whisk together all the BBQ sauce ingredients from the tomato paste to black pepper in a medium bowl until smooth and well combined.
Layer the thinly sliced onions evenly at the bottom of a 4-quart or larger slow cooker.
Arrange the chicken pieces on top of the onions in the slow cooker.
Pour the prepared BBQ sauce mixture evenly over the chicken and onions.
Cover and cook on HIGH for 3 to 4 hours or on LOW for 5 to 6 hours until chicken is tender.
Transfer the cooked chicken onto a large plate or sheet pan.
Use two forks, a meat shredder, or shredder claws to pull the chicken apart into bite-sized pieces.
Return the shredded chicken to the slow cooker and mix well to coat all the chicken with the sauce.
Keep the slow cooker on the WARM setting to maintain heat until ready to serve.