Place chicken in the bottom of the slow cooker.
Add the garlic, onion, and seasonings and mix well to evenly coat the chuck roast.
Pour in the broth, lime juice, and apple cider vinegar. Mix thoroughly.
Cover the slow cooker and set to high for 4 hours or low for 6-8 hours until the chuck roast easily shreds with a fork.
Remove the bay leaves from the slow cooker and shred the barbacoa.