Proof yeast with warm water and sugar. Mix dry ingredients in a large bowl. Add liquids and yeast, knead thoroughly, adding more water or flour until dough is firm. Leave dough in covered bowl for 30 minutes in a warm location. Roll dough out onto cornmeal-coated pizza stone or a glass or metal cookie sheet coated with olive oil. Let rise an additional 30 minutes.
Mix together sauce ingredients and simmer for 5-10 min then spread over crust, then cover with cheese. Top with chicken then onion and cilantro. (If using a pre-made crust, precook the chicken and reduce baking time to 20 minutes.) Bake at 350 F to 375 F for 30-45 minutes or until chicken is done. Remove from oven and let cool for 10 minutes before serving.