Place a baking stone on the bottom rack of the oven and preheat to 450°F.
Place one ball of dough on a large sheet of parchment and shape and stretch until you have a thin 12-inch circle. To get the dough super thin, briefly roll with a rolling pin. Slide the dough to a pizza peel or flat cookie sheet. Cover with a clean towel until ready to use.
Brush the olive oil onto the edges of the pizza dough. Spread the pesto over the dough. Sprinkle with the mozzarella cheese. Sprinkle with the asparagus and tomatoes. Season to taste with salt and pepper. Slide the dough onto the baking stone, keeping the parchment underneath the dough. Bake for about 12 to 14 minutes, or until the cheese is bubbling and the dough is golden. Sprinkle with the chives and let cool for 5 minutes before slicing and serving.