In a 5-quart slow-cooker, combine chuck roast, onion, garlic, lime juice, chili powder, cumin, and oregano, then pour over chicken broth. Cover and let cook on low, 8 hours.
When ready to shred, add roast and onion to a large bowl and shred with two forks. Pour over enough juice so it's nicely marinated.
Char tortillas over the flame of a gas burner, then top with beef and serve with sour cream, green onions, chopped red onion, and limes.
