The 10,000-year-old remains of 27 people found west of Lake Turkana show that they met violent deaths.
They were left to die there rather than being buried.
Many experts have argued that conflict only came about as humans became more settled.
These people, by contrast, were apparently nomadic hunter-gatherers.
The archaeologists, who have been working on the site at Nataruk since 2012, discovered that the victims were clubbed or stabbed to death in a single event.
The dead included male and female adults, as well as children.
The evidence, published in the journal Nature, does not reveal exactly what happened but the fact that so many people died at the same time suggests it was the result of "some sort of conflict", according to Cambridge University Professor Robert Foley.
Nataruk records what is, for now, the oldest scientifically-dated case of conflict between two nomadic hunter-gatherer groups.
Nevertheless, its significance is not its age, but the fact that it involved these groups, who had few possessions to fight over.
Nataruk establishes definitively that inter-group violence can and did arise regardless of whether the populations were settled.
All it needed was moments of food abundance, causing groups to grow in size, putting pressure on the resources. Then the benefits of stealing from another group could outweigh the costs of the conflict that might ensue.
Nataruk was an important place because it was at the edge of a super lake beach which would have attracted all land animals to drink, as well as giving access to fishing grounds, while other parts of the shore of Lake Turkana (the forested Kerio Delta, for example, or the rocky whole southern edge) would not have that.
It is believed that the group was attacked by rival hunter-gatherers armed with wooden clubs and arrows or spears tipped with sharpened obsidian, a rare black volcanic rock.
Speculating on the causes of the attack, Marta Mirazon Lahr, who led the Nataruk study, said the "massacre may have resulted from an attempt to seize resources... whose value was similar to those of later food-producing agricultural societies, among whom violent attacks on settlements became part of life".
Today, the area where the bodies were found is scrubland, but the researchers say that 10,000 years ago it would have been fertile and very close to the shoreline of the lake.
Many experts have argued that conflicts only arise "once people have things worth fighting over, [such as] herds of livestock, stores of grain... things that you can both defend and attack," Professor Foley told the BBC's Newsday radio programme.
It has been assumed that hunter-gatherers were less likely to engage in such conflicts because they can move away, but the Nataruk find shows that "before we have settled life, groups were competing over resources", Professor Foley added.

Jac Davies died following a blaze at his family home in Alltwen, Neath Port Talbot, in the early hours of July 27.
His mother Jenny, 28, escaped the fire with her 11-month-old baby and daughter Kelsey, six, while other son Riley, three, was rescued by a firefighter.
An inquest into Jac's death was adjourned last month.
South Wales Police have confirmed a woman was arrested and bailed last month in connection with the incident.
Police have not named the woman involved but it is understood to be Jac's mother.
A spokesman said: "A 28-year-old woman from the Pontardawe area has been arrested on suspicion of child neglect and is currently on police bail while enquiries continue."
A pre-inquest into Jac's death will be held on January 25.
Archaeologists say they have unearthed the earliest evidence of warfare between hunter-gatherers to be scientifically dated, at a remote site in northern Kenya.
[NEXT_CONCEPT]
The mother of a four-year-old boy who died in a house fire has been arrested on suspicion of child neglect.