Preheat oven to 425°F. If you have a baking stone, place it in the oven to pre-heat.
Using flour as needed, roll out one ball of pizza dough until thin (thin enough so the dough isn't in danger of tearing), about 12 inches across. Transfer the dough to a sheet pan or hot baking stone. Spoon 1/2 cup tomato sauce and 1/4 cup BBQ sauce onto dough. Add half of the sliced mozzarella and half of the chopped chicken.
Bake for 10 to 15 minutes, or until dough is crisp and cheese is melted. Repeat with remaining dough for second pizza, or bake the pizzas side-by-side if your oven is big enough.
Garnish pizzas with cilantro and green onions, and serve while hot.