I want to say it was Cain's sarcastic remark to God, "am I my brother's keeper?"
As usual, though, those killjoy historians think they know better. A team from the University of Wolverhampton researched this question for a British TV show in 2008. The oldest joke they could find with a setup and punchline was the four-thousand-year-old Sumerian proverb: "Something which has never occurred since time immemorial; a young woman did not fart in her husband’s lap."
An interesting collection of ancient humour is a book called Philogelos, or The Laugh Addict, an anthology of several hundred jokes from the 4th or 5th Century CE.
A man goes up to a student dunce and says, 'The slave you sold me died.' 'By the gods,' counters the dunce, 'when he was with me, he never did any such thing!'
A sharp-witted fellow is watching a really dumb literature teacher at work. He approaches him and asks, 'Why aren't you teaching the lyre?' 'I don't know how to play the lyre,' answers the teacher. 'Then how is it you're teaching literature, when you don't know how to read?'
A drunk is being railed at for losing touch with reality when he's had a snootful. Barely able to see straight because of the wine, the drunk retorts, 'Who's the drunk here, you or me—you two-headed freak!'
"Something which has never occurred since time immemorial; a young woman did not fart in her husband's lap." Which is bad sentence structure, but I think it's basically saying wives fart in their husband's laps a lot?
Anyways, you can find a pretty interesting article about the study in which this was published (written by the author) here! http://www.independent.co.uk/voices/commentators/paul-mcdonald-heard-the-one-about-the-oldest-joke-in-the-world-its-a-cracker-2164293.html
I'll adapt a previous answer I made in order to elaborate on /u/thebulgarslayer's correct answer:
As far as I am aware, the oldest joke is from 1900 BC Sumer and goes like this:
"Something which has never occurred since time immemorial; a young woman did not fart in her husband's lap."
Another very old joke comes from 1600 BC Egypt, attributed to Pharaoh Snofru:
"How do you entertain a bored pharaoh? You sail a boatload of young women dressed only in fishing nets down the Nile and urge the pharaoh to go catch a fish."
The study was conducted by students and faculty at the University of Wolverhampton under the auspices of Dr. Paul McDonald, and was commissioned by the TV channel Dave in an attempt to understand the ancient origins of humor.
http://uk.reuters.com/article/2008/07/31/uk-britain-joke-life-idUKL129052420080731