The Shroud of the Sword was an ancient cloth in which the Sword of Kahless was wrapped. Both the shroud and the sword itself were stolen by the Hur'q, when they plundered Qo'noS in the 14th century, and taken to the Gamma Quadrant.
Over the centuries, numerous forged copies of the Shroud were produced by unscrupulous peddlers. The true Shroud was accidentally discovered among some ruins by a Vulcan bakrinium mining expedition in 2372. At the time, the Vulcans were unaware of the artifact's importance. When Kor, the ambassador to Vulcan, recognized Hur'q markings on the Shroud, he convinced the Vulcans to give the cloth to him as a gift. He took it to Deep Space 9 to have Jadzia Dax verify its authenticity, and then embarked on a quest to find the Sword itself. (DS9: "The Sword of Kahless")