A computer program called Eugene Goostman, which simulates a 13-year-old Ukrainian boy, is said to have passed the Turing test at an event organised by the University of Reading.
The test investigates whether people can detect if they are talking to machines or humans.
The experiment is based on Alan Turing's question-and-answer game Can Machines Think?
No computer has passed the test before under these conditions, it is reported.
However, some artificial intelligence experts have disputed the victory, suggesting the contest had been weighted in the chatbot's favour.
The 65-year-old Turing Test is successfully passed if a computer is mistaken for a human more than 30% of the time during a series of five-minute keyboard conversations.
On 7 June Eugene convinced 33% of the judges at the Royal Society in London that it was human.
Judges included actor Robert Llewellyn, who played an intelligent robot in BBC Two's science-fiction sitcom Red Dwarf, and Lord Sharkey, who led the successful campaign for Alan Turing's posthumous pardon, over a conviction for homosexual activity, in 2013.
Eugene was created by Vladimir Veselov, who was born in Russia and now lives in the United States, and Ukrainian-born Eugene Demchenko, who now lives in Russia.
Transcripts of the conversations are currently unavailable, but may appear in a future academic paper.
The judges and hidden human control groups were kept apart throughout the test.
The event was organised by Reading University's School of Systems Engineering in partnership with RoboLaw, an EU-funded organisation examining the regulation of emerging robotic technologies.
Alan Turing was an English mathematician, wartime code-breaker and pioneer of computer science.
The event has been labelled as "historic" by the organisers, who claim no computer has passed the test before.
"Some will claim that the Test has already been passed," said Kevin Warwick, a visiting professor at the University of Reading and deputy vice-chancellor for research at Coventry University.
"The words Turing test have been applied to similar competitions around the world. However, this event involved the most simultaneous comparison tests than ever before, was independently verified and, crucially, the conversations were unrestricted.
"A true Turing test does not set the questions or topics prior to the conversations. We are therefore proud to declare that Alan Turing's test was passed for the first time on Saturday."
Prof Noel Sharkey, a leading expert in robotic technology and artificial intelligence, said: "It is indeed a great achievement for Eugene. It was very clever ruse to pretend to be a 13-year-old Ukranian boy, which would constrain the conversation. But these competitions are really great to push developments."
But others have criticised the claim.
"It's nonsense," Prof Stevan Harnad told the Guardian newspaper. "We have not passed the Turing test. We are not even close."
Hugh Loebner, creator of another Turing Test competition, has also criticised the University of Reading's experiment for only lasting five minutes.
"That's scarcely very penetrating," he told the Huffington Post, noting that Eugene had previously been ranked behind seven other systems in his own 25-minute long Loebner Prize test.