Preheat oven to 400ºF. Set pizza crust on an ungreased sheet pan and set aside. Halve the onions and slice lengthwise into thin strips. Heat the butter or oil in a skillet over medium-high heat. Add onions to pan and cook, stirring often, for approximately six minutes until beginning to brown. Add the sugar and season onions to taste with salt and pepper. Reduce heat to medium. Continue to cook until onions are soft and dark brown, stirring frequently, about 10 minutes. Add one tablespoon of water to the pan and stir the onions, scraping up any bits from the bottom of the pan. Once the water evaporates, remove from heat and set aside. Meanwhile, combine the cheeses in a small bowl. Lightly brush the crust with olive oil and spread two-thirds of the cheese mixture evenly over crust. Top with chicken and caramelized onions, and sprinkle the remaining cheese mixture over top. Cook for 10-13 minutes until cheese is bubbly. For a crisper crust, remove the pizza from the sheet pan the last few minutes of cooking. Cool slightly before slicing.