
In a 6- to 8-quart slow cooker, whisk together the BBQ sauce, vinegar, brown sugar, paprika, salt, black pepper, cayenne pepper, garlic, and onion until well combined. Add the chicken, stirring to ensure it is fully coated with the sauce sauce.
Cover and cook until the chicken is tender and shreds easily, on low for 4 to 6 hours or on high for 2 to 3 hours.
Remove the chicken to a large cutting board. Remove the garlic cloves, if you like. Using 2 forks, break up the chicken into chunks (or shred it more finely, if you like). Return the chicken to the sauce and stir very well.
Cover and cook on low for 30 minutes more. Taste and add more salt or vinegar, if you like.