Combine Monterey Jack Cheese Sauce and Shredded Monterey Jack Cheese with Jalapeños in saucepan. Heat over medium-low heat, stirring occasionally, until shreds are melted; hold hot until service.
Mix chicken and barbecue sauce until well coated. Heat; hold hot until service.
To build, layer half of hot fries on serving platter. Top with half each of chicken, cheese sauce, bacon, tomato, pickle and onion. Layer remaining fries and all remaining ingredients. Serve immediately.