Preheat oven to 425 degrees F. In a large skillet cook onion in 1 tablespoon hot oil over medium heat for 10 minutes until softened, stirring occasionally. Set aside.
In a small bowl combine remaining 3 tablespoons oil and crushed red pepper; drizzle some of the oil mixture onto the pizza crusts. Place crusts on a very large baking sheet(s). Top with chicken, onion, and cheese.
Bake for 10 minutes or until cheese is melted and pizzas are heated through.
Top pizzas with arugula, drizzle any remaining oil, and sprinkle or pass additional crushed red pepper.