1. Place oven rack on lowest shelf. If you have a stone, place it on rack. Preheat oven to 550°F, or the highest temperature your oven allows, for 45 minutes.
2. Dust a 14-inch pizza peel with cornmeal, then flatten dough on top. Using lightly floured fingers or a floured rolling pin, stretch dough into a 13- to 14-inch round. (Sprinkle peel with more cornmeal if necessary to make sure crust slides around easily on peel.) Brush oil over surface of crust.
3. Sprinkle half of cheese on dough, leaving a 1-inch border. Toss chicken with 1 Tbsp. barbecue sauce. Spoon remaining sauce in a spiral over cheese. Scatter chicken, remaining cheese and half of scallions on pizza.
4. Carefully slide pizza onto stone. Bake until crust is just slightly charred on top and golden on bottom (lift an edge of pizza to check) and cheese is melted and bubbling, 8 minutes. Using peel, transfer pizza to a cutting board. Sprinkle remaining scallions over pizza. Let pizza rest for a minute or 2, then slice and serve.