Remove skin from chicken and place chicken in a 6-quart or larger slow cooker. Sprinkle onion on top.
In a small bowl, combine butter, oil, paprika, garlic powder, salt, pepper, and liquid smoke. Pour over chicken.
Cover slow cooker and cook on LOW for 5 hours or on HIGH for 3 hours.
Meanwhile, make sauce. Whisk together all ingredients in a medium bowl. Cover and refrigerate.
When chicken is done, remove it from the slow cooker. Discard all of the liquid in the slow cooker, except ¼ cup. (You can discard the onions or return them to the slow cooker.)
Shred the chicken, discarding the bones. Return chicken to the slow cooker along with the ¼ cup liquid. Mix in ⅓ cup of sauce. Leave on WARM until ready to serve.
Serve with additional sauce.
