In a large bowl, whisk together the instant chocolate pudding mix and cold milk until thickened. Set aside to chill.
In another bowl, beat cream cheese until smooth, then mix in the sweetened condensed milk. Gently fold in whipped topping until fully combined.
In a 9x13-inch dish, arrange a layer of Chessmen cookies, followed by a layer of sliced bananas. Spread half of the cream mixture, then spoon over the chocolate pudding. Top with remaining cream mixture and a final layer of cookies.
Cover and refrigerate for at least 4 hours or overnight to allow cookies to soften and flavors to blend.