In a small bowl, combine the first 8 ingredients. Stir well with a whisk and set aside. In a medium nonstick skillet coated with cooking spray, cook chicken over medium heat until browned, about 2 minutes. Remove chicken from the pan.
Pour the rice vinegar mixture into the pan and bring to a boil over medium-high heat. Cook the mixture until it thickens to a syrup, about 6 minutes. Return the chicken to the pan and cook until chicken is fully cooked through, about 1 minute.
Position an oven rack at the bottom of the oven and preheat to 500 degrees F.
Sprinkle the cheeses over the pizza crust, leaving a 1-inch border, and top with the chicken. Bake for 12 minutes on the bottom rack of the oven. Remove from the oven and sprinkle with green onions. Place pizza on a cutting board and let stand for 5 minutes before serving.
In a small pot, warm the water to 100 to 110 degrees F. In a large bowl, dissolve sugar and yeast in warm water and let stand for 5 minutes.
Lightly spoon flour into dry measuring cups and level with a knife. Add flour, cornmeal, oil and salt to yeast mixture; stir until soft dough forms. Turn dough out onto a floured surface and knead until even, about 5 minutes. Add bread flour as needed to prevent dough from sticking to hands. Place dough in a large bowl coated with cooking spray and turn to coat.
Cover and let rise in warm place (about 85 degrees F) free from drafts until doubled in size, about 45 minutes. Gently press 2 fingers into dough; if indentation remains, dough has risen enough. Punch dough down into the shape of a ball.
Lightly re-spray bowl; place dough in bowl, turning to coat again. Cover; let the dough rise again in a warm place (about 85 degrees F) free from drafts for another 30 minutes.
Place the dough on a lightly floured surface and roll out to a 12-inch crust. Top the dough according to pizza instructions.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.