A research paper published in Thermochimica Acta suggests the shroud is between 1,300 and 3,000 years old.
The author dismisses 1988 carbon-14 dating tests which concluded that the linen sheet was a medieval fake.
The shroud, which bears the faint image of a blood-covered man, is believed by some to be Christ's burial cloth.
Raymond Rogers says his research and chemical tests show the material used in the 1988 radiocarbon analysis was cut from a medieval patch woven into the shroud to repair fire damage.
It was this material that was responsible for an invalid date being assigned to the original shroud cloth, he argues.
"The radiocarbon sample has completely different chemical properties than the main part of the shroud relic," said Mr Rogers, who is a retired chemist from Los Alamos National Laboratory in New Mexico, US.
Fire damage
He says he was originally dubious of untested claims that the 1988 sample was taken from a re-weave.
"It was embarrassing to have to agree with them," Mr Rogers told the BBC News website.
The 4m-long linen sheet was damaged in several fires since its existence was first recorded in France in 1357, including a church blaze in 1532.
It is said to have been restored by nuns who patched the holes and stitched the shroud to a reinforcing material known as the Holland cloth.
"[The radiocarbon sample] has obvious painting medium, a dye and a mordant that doesn't show anywhere else," Mr Rogers explained.
"This stuff was manipulated - it was coloured on purpose."
In the study, he analysed and compared the sample used in the 1988 tests with other samples from the famous cloth.
In addition to the discovery of dye, microchemical tests - which use tiny quantities of materials - provided a way to date the shroud.
These tests revealed the presence of a chemical called vanillin in the radiocarbon sample and in the Holland cloth, but not the rest of the shroud.
Vanillin is produced by the thermal decomposition of lignin, a chemical compound found in plant material such as flax. Levels of vanillin in material such as linen fall over time.
'Older date'
"The fact that vanillin cannot be detected in the lignin on shroud fibres, Dead Sea scrolls linen and other very old linens indicates that the shroud is quite old," Mr Rogers writes.
"A determination of the kinetics of vanillin loss suggests the shroud is between 1,300 and 3,000 years old."
In the 1988 study, scientists from three universities concluded that the cloth dated from some time between 1260 and 1390. This ruled it out as the possible burial cloth that wrapped the body of Christ.
That led to the then Cardinal of Turin, Anastasio Alberto Ballestrero, admitting the garment was a hoax.
Michael Minor, vice-president of the American Shroud of Turin Association for Research, commented: "This is the most significant news about the Shroud of Turin since the C-14 dating was announced in 1988.
"The C-14 dating isn't being disputed. But [the new research] is saying that they dated the rewoven area."
But since the announcement of the 1988 results, several attempts have been made to challenge the authenticity of these tests.
"The sample tested was dyed using technology that began to appear in Italy about the time the Crusaders' last bastion fell to the Mameluke Turks in AD 1291," said Mr Rogers.
"The radiocarbon sample cannot be older than about AD 1290, agreeing with the age determined in 1988. However, the shroud itself is actually much older."
Some now hope the Vatican will give approval for samples of the shroud to be re-tested.
But, says Mr Minor, "the church is very hesitant, very reluctant for that to be done, because they've been given so many conflicting opinions".
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