Handedness, a uniquely human trait, signals brain lateralisation, where each of the brain's two hemispheres is specialised.
The left brain controls the right side of the body and plays a primary role for language.
So, if Neanderthals were primarily right-handed, that fact could suggest a capacity for language, the Daily Mail reported.
There are few Neanderthal skeletons available to science.
One of the more complete was discovered in 1957 in France, roughly 900 yards away from the famous Lascaux Cave.
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That skeleton was dubbed 'Regourdou' and, about two decades ago, researchers examined his arm bones and theorised that he had been right-handed.
"This skeleton had a mandible and parts of the skeleton below the neck," David Frayer, professor of anthropology at the University of Kansas, said.
"Twenty-plus years ago, some people studied the skeleton and argued that it was a right-handed individual based on the muscularity of the right arm versus the left arm," he said.
Now a new investigation by Professor Frayer and an international team led by Virginie Volpato of the Senckenberg Institute in Frankfurt, Germany, has confirmed Regourdou's right-handedness by looking more closely at the robustness of the arms and shoulders, and comparing it with scratches on his teeth.
"We've been studying scratch marks on Neanderthal teeth, but in all cases they were isolated teeth, or teeth in mandibles not directly associated with skeletal material," Frayer said.
"This is the first time we can check the pattern that's seen in the teeth with the pattern that's seen in the arms. We did more sophisticated analysis of the arms, the collarbone, the humerus, the radius and the ulna, because we have them on both sides. And we looked at cortical thickness and other biomechanical measurements," he said.
"All of them confirmed that everything was more robust on the right side then the left," he added.
Frayer said that the research on Regourdou shows that 89 per cent of European Neanderthal fossils (16 of 18) showed clear preference for their right hands.
This is very similar to the prevalence of right-handers in modern human populations, about 90 per cent of people alive today favour their right hands.
Professor Frayer and his co-authors conclude that such ratios suggest a Neanderthal capacity for language.
Their findings were published yesterday in the journal PLOS ONE.