DMZ2112
Chaotic Looseleaf
Will they? What kind of true code would a chaotic good/neutral/evil paladin even follow? Better yet why would a chaotic character ever be bound by a code, isn't that a lawful behavior? And if he or she wouldn't, why can a chaotic character be a paladin (outside of the "because we dropped alignment restrictions" reason)?
If a player wants to play a chaotic paladin, it is up to him to devise a code that describes his character's ideals and that satisfies the dungeon master that the class' requirements have been met. If he cannot, that player will not be playing a paladin.
If this means that by your metric all paladins are lawful, then so be it. No one at your table will be playing a chaotic paladin. But for my part, if chaos were as simply defined as "effect without cause," all chaotic characters would be psychotic jesters.