Turn on your grill to medium heat.
Set a large heat proof skillet over med-high heat; add in chicken, barbecue sauce, beans, corn, and sour cream; stir to combine.
Cook until hot, 4-5 minutes.
Assemble wraps by placing a lettuce leaf in the center of each tortilla and top with ¼ of the chicken mixture.
Roll as you would a burrito.
If you want grill marks, carefullly transfer to grill and let cook for another 2 minutes over direct heat.
Slice in half diagonally and serve warm with lime wedges.