In a small bowl combine the paprika, chipotle powder, thyme, salt, pepper, onion powder and garlic powder. Set aside. In a separate bowl whisk together the sugar, lime juice and zest, soy sauce, and rice vinegar.
Add the chuck roast to your slow cooker and massage both sides with the dry rub, making sure to get in between any folds of the meat. Add the lime juice mixture, beef broth, and bay leaves to the slow cooker. Set slow cooker to high and cook for at least 5-6 hours.
After the beef is fully cooked, remove meat from the slow cooker and shred with two forks. Transfer back to the slow cooker and add 1/2 cup teriyaki sauce. Mix well to combine. Switch slow cooker to low and continue to cook until ready to serve.