As much as Batman is Gotham's spirit, so is The Joker. Dark, violent Order and Dark violent Chaos, both working efficiently outside of the usual system (Police and organised crime). In fact, over time Joker may well have killed more "bad guys" than the Batman has ever detained.
Joker, we would all agree, is obsessed with Batman. Frank Miller has shown us that the Joker ceases to function without The Batman. Are these the actions of an agent of Chaos? Surely if he were an insane homicidal maniac, he would simply find a new target?
There is a reason The Joker loses the will to commit crime when Batman isn't around:
The Joker exists only to make Batman better at what he does.
Think of all of the skills and equipment added to Batman's arsenal due to situations Joker has put him in, only to re-use those tactics/weapons against a future adversary.
When Joker goes to Arkham, the inmates fill their time by talking, mainly about how they're going to take Batman down. And who knows where he disappears to every time he's assumed dead? Wherever he is, he is well resourced and well connected, with an ear to the criminal under ground.
The Joker believes in The Batman. He believes in him enough to sacrifice anything; innocent lives, Batman's colleagues, whatever it takes to make Batman tougher. When he finds out something is coming Batman's way that he might not be able to handle? Joker attacks with the same technique, but taken down a level. Not enough to kill Batman just enough to train Batman for the oncoming storm.
The Joker isn't Batman's archenemy, Joker is Batman's coach, personal trainer and biggest cheerleader.
You singlehandedly crafted the greatest, most resilient crime fighter of all time Mr J. Take a bow.