Combine marinade ingredients in a large bowl. Place chuck in marinade and cover with plastic wrap. Place in refrigerator and allow marinating between 4-6 hours, or overnight.
Preheat grill to 375 degrees. Remove chuck from marinade and place over indirect heat. Cover lid and allow cooking for 50-65 mins, depending on personal preference for rare vs. well done.
Remove from grill and place on cutting board. Using the Outset Meat Shredders, shred meat.
Garnish with lime juice and lime wedge. Serve and enjoy!