The popular answer to this question is Jack the Ripper, and while he is certainly the most famous, the psychological underpinnings of serial killers have to have existed longer than 100 years.
The earliest well documented case I'm aware of is Liu Pengli (second century BC), a prince of the Han dynasty. He was known to go out at night in the company of slaves or outlaws to murder and steal. It was well known by the people of the Jidong province. He preformed these nightly "raids" for a long time without being reported, most likely because he was the nephew of the Emperor Jing.
He was finally reported to the Emperor by the son of one of this victims. The investigation found that he had killed well over 100 people. He was never executed for his crimes but stripped of title and land and made a commoner. I was somewhat hesitant to include him because he is perhaps more of "robber Baron" than a serial killer.
The story is documented in The Book of Former Han from 111 AD.