In the bowl of your slow cooker combine the chuck roast pieces, onions, garlic, green chilies, chipotles, ground cumin, oregano, salt, and pepper.
In a small bowl, whisk together the beef broth, vinegar, and lime juice; pour the broth mixture over the ingredients in the slow cooker. Add bay leaves.
Cover and cook on LOW for 6 to 8 hours, or on HIGH for 3 to 4 hours. Cooked beef should be tender and should fall apart easily when shredded with a fork.
Remove the beef from the slow cooker and transfer it to a cutting board.
Using two forks, or shredder claws, shred the beef into bite-size pieces.
Transfer the shredded beef back into the slow cooker; stir everything together until completely incorporated.
Garnish with cilantro or parsley and serve.