The Shroud of Turin
The Shroud of Turin has been a controversial piece of cloth for centuries. The shroud is considered one of the holiest relics by Catholics, who believe the cloth was Jesus' burial shroud and bears the image of his face. But there is nothing but faith as confirmation of its legitimacy, and in 1988 carbon-14 dating testing found fibers in the linen cloth were from the Middle Ages, confirming for the scientific community the shroud was a forgery and not from the time of Jesus' crucifixion.
In 2005, however, new findings that the cloth is actually between 1,300 and 3,000 years old were published in Thermochimica Acta [source: BBC News]. This suggests that the shroud was much older than the estimates from the 1980s, which dated the shroud from between 1260 and 1390 A.D. -- a mistake that's being blamed on samples taken from a patch in the linen rather than from the original cloth for the 1988 carbon testing.
While the legitimacy of the shroud is still unknown, the church does allow for rare appearances, even after the 1988 forgery claims. The shroud was seen on TV in 2013, but prior to that hadn't been given a public viewing since 1973.