Writer Grant Morrison believes it is.
Speaking to Kevin Smith on a recent podcast, Morrison says that he believes that Batman killed the Joker thirty years ago in writer Alan Moore’s influential The Killing Joke.
“That’s what I love about [the book],” Morrison tells Smith. “No one’s noticed — however much, 30 years on, almost — Batman kills the Joker. That’s why it’s called The Killing Joke. The Joker tells the ‘Killing Joke’ at the end, Batman reaches out and breaks his neck, and that’s why the laughter stops and the light goes out, ’cause that was the last chance at crossing that bridge. And Alan Moore wrote the ultimate Batman/Joker story. He finished it… but he did it in such a way that it’s ambiguous, so people will never have to be sure, which means it doesn’t have to be the last Batman/Joker story. It’s brilliant!”
Looking at the original comic, Morrison’s assertion could be supported by the visual evidence. In the final panels of the comic, the Joker offers to tell Batman a joke and begins to laugh. The Dark Knight joins the laughter and leans in toward the Joker. At this point, both characters are seen in silhouette and it could be that Batman is leaning on the Joker because he’s laughing so hard or it could be taken that the Dark Knight is finally ending his long running battle with his enemy and killing the Joker. As the focus of each successive panel moves away from the characters toward raindrops hitting a puddle, the laughter stops abruptly, but the sound effect of a nearby police siren continues.
Does the sudden end to the laughter signify the sudden end of the Joker? On the one hand, obviously not — the character continued to appear in storylines following The Killing Joke for years afterward, including multiple stories that explicitly referenced The Killing Joke, ensuring that no “imaginary story” or alternate world explanation could explain away the possible discrepancy. But did Moore intend for the story to end with the Joker’s death?