Heat the oil in a skillet over medium heat. Stir in the onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Reduce heat to medium-low, and continue cooking and stirring until the onion is very tender and dark brown, 15 to 20 minutes more.
Place the bacon in a large, deep skillet, and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain the bacon slices on a paper towel-lined plate; crumble when cool.
Preheat an oven to 425 degrees F (220 degrees C). Grease a baking sheet.
Press the refrigerated pizza crust onto the baking sheet to fit the size of the pan. Spread the barbeque sauce evenly over the dough, and sprinkle with the shredded chicken, caramelized onion, bacon, Gorgonzola cheese, and diced jalapeno pepper. Season with paprika and garlic powder. Top with the shredded mozzarella cheese.
Bake in the preheated oven until the cheese has melted and is bubbly and the pizza dough is golden brown on the bottom, 15 to 17 minutes.