Set a pizza stone on an oven rack and preheat the oven to 425 degrees F. Roll out and stretch the dough on parchment paper or a pizza peel to a 12-inch circle; set aside.
Melt the butter in a medium saucepan over medium-low heat and whisk in the hot sauce. Pour half the mixture into a medium bowl, add the chicken and stir to coat fully. Pour any excess sauce back into the saucepan.
Ladle a few tablespoons of the remaining hot sauce mixture on the dough and spread in a thin even layer. Scatter with the chicken and mozzarella. Sprinkle the blue cheese on top.
Transfer the pizza to the preheated pizza stone and cook until crisp, 12 to 15 minutes. Garnish with the scallions, and drizzle the remaining sauce over the top.