Edgar Allan Poe's "Murders in the Rue Morgue?" Sorry. Published in 1841, that's practically current events.
How about Shakespeare? There was that whiny prince trying to figure out who killed his father. Uh uh. Hamlet only goes back to 1600.
Well, there was the story of Susannah, which appears in some editions of the Book of Daniel. The prophet solves a crime by using a technique known to every modern police force. But that only dates back to around 200 BC.
How about Sophocles' play about a king interrogating various witnesses to discover the murderer of his predecessor? Nice guess, but no. At 400 BC, he's still an Oedipus-come-lately.
Enough suspense. Here is the true answer, courtesy of those brilliant British comedians David Mitchell and Robert Webb.