SPOILERS AHOY FOR ANYONE READING DC COMICS!
It apppears, The Joker is an immortal....
It seems that The Joker was one of three people who came into contact with the mysterious meteroite that gave Vandal Savage his immortality (and Ra's Al Ghul has been making the Lazarus Pits from a compound made of this meteorite too?)
This lead to the shocking revelation that The Joker has also encountered the meteorite long before Gotham ever even existed.
“For me, I wanted to make something that felt real and was believable, while at the same time was mythologically big and epic, the way the story is, so that it is material that might have been here and might have done this to Vandal Savage and might be the basis for the Lazarus Pit, or Electrum — which is what keeps the Owls coming back from the dead, the Talons. It might have something to do with other figures as well, for Solomon Grundy… I wanted to create something that links all that. So the Joker says, “I knew this. I knew this part of it. I’m older than Gotham. I’m the Pale Man that walks these shores, and I’ve seen all of it. I’m the immortal person here. You are nothing. I let you believe it for a little while because I wanted you to come with me and become something important, but you had your chance in Death of the Family, and you threw me off a goddamn cliff. So… you’re done.”