Preheat oven to 350°F. Melt butter in a medium sauté pan over medium-low heat. Add chicken and hot sauce. Cook, stirring, until warm. Add cream cheese, cheddar, and half the blue cheese, and stir until combined. Transfer to an oven-safe 2 cup baking dish.
Bake until bubbling, 24 to 26 minutes. Serve garnished with chives and remaining blue cheese and crudités alongside.
