Combine first 8 ingredients in a bowl; stir well with a whisk.
Heat a nonstick skillet coated with cooking spray over medium heat. Add chicken, and sauté 2 minutes. Remove chicken from pan.
Pour rice vinegar mixture into pan, and bring to a boil over medium-high heat. Cook mixture 6 minutes or until slightly thickened. Return chicken to pan; cook 1 minute or until chicken is done. (Mixture will be consistency of thick syrup.).
Sprinkle cheeses over prepared crust, leaving a 1/2-inch border, and top with chicken mixture. Bake at 500° for 12 minutes on bottom rack in oven. Sprinkle with green onions. Place pizza on a cutting board; let stand 5 minutes.
Dissolve sugar and yeast in water in a large bowl, and let stand 5 minutes. Stir in 2 3/4 cups flour, salt, and olive oil to form a soft dough.
Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 5 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands.
Place dough in a bowl coated with cooking spray, turning to coat. Cover; let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size. (Press two fingers into dough. If indentation remains, dough has risen enough.).
Punch dough down; divide in half. Roll each half into a 12-inch circle on a lightly floured surface. Place dough on 2 (12-inch) pizza pans or baking sheets each coated with cooking spray and sprinkled with 1/2 tablespoon cornmeal. Crimp edges of dough with fingers to form a rim. Cover; let rise in a warm place (85°), free from drafts, for 30 minutes.
Note: To save half of dough for later, wrap in plastic wrap, and store in a zip-top heavy-duty plastic bag in freezer. To thaw, place dough in refrigerator 12 hours or overnight; bring to room temperature, and shape as desired.