First, preheat the oven to 350°. Grease an 8 x 11 casserole dish and set it aside.
Then, bring a large pot of salted water to a boil. Add the pasta and cook it according to the package instructions.
Meanwhile, while the pasta is cooking, heat the butter and olive oil in a large skillet over medium heat. Once the pan is hot, add the chicken pieces.
Cook the chicken until browned on both sides and cooked through. Add the onions and stir. Cook until the onions have softened.
Meanwhile, while the chicken and pasta are cooking, stir together the cream cheese, BBQ sauce, mayonnaise, and ¼ cup of the shredded mozzarella in a large mixing bowl.
Then, add the warm cooked pasta to the bowl with the BBQ sauce mixture. Stir it well to coat the noodles.
Next, add the cooked chicken and onions to the bowl with the sauce and pasta. Stir it all well to combine.
Then, spread the mixture evenly into the prepared baking dish. Cover it with the remaining ¾ cup of shredded mozzarella.
Bake in the preheated oven for 15-20 minutes until the cheese is melted and bubbling.
Serve warm.