Combine cumin, oregano, garlic, and marinade in a bowl or bag; add chicken. Marinate at least 1 hour or up to 4 hours.
Grill chicken over medium heat, about 4 minutes per side.
Once cooked, remove chicken from the grill and let rest 3 minutes. Chop into ½-inch cubes.
Meanwhile, warm tortillas in the microwave or in a skillet. Top tortillas with chicken and toppings as desired.Note: Extended marinating time needed for this recipe.