In a small bowl, toss shredded chicken with half of the BBQ sauce. Set aside.
While you're preheating the grill, roll out your dough on a lightly floured 9-inch pizza pan. Gently stretch it and pull it to fit the 9-inch pizza pan.
Once done, place it gently on the grill (you may need a helping hand for this part). Close the lid and grill for 3-5 minutes on each side (checking every so often to make sure the bottom doesn't get too charred - every grill VARIES in temperature so keep an eye on it).
After 3-5 minutes, flip the dough on the other side, close the lid and grill for another 3-5 minutes, again checking every so often to make sure it doesn't get too charred.
Once both sides have been grilled, bring the dough inside to assemble your toppings.
Brush a thin layer of BBQ sauce on top of the dough then sprinkle red onion, blue cheese, shredded chicken, and basil on top.