Preheat the oven to 350ºF and lightly spray a 9×13-inch baking dish with cooking spray.
Remove the skin from the rotisserie chicken, pull the meat from the bones, discard the bones, chop the chicken, and spread the chopped chicken in the bottom of the prepared baking dish.
Prepare the stuffing mix according to package directions and set it aside.
In a bowl, combine the sour cream, cream cheese, and Unsalted Cream of Chicken Soup with the chopped broccoli; spread the mixture evenly over the chicken.
Top the casserole evenly with the prepared stuffing.
Bake uncovered for 30 minutes.