Similar to the Romulan cloaking device, the Klingons received this technology from the Romulans circa 2268, when the two civilizations shared a political alliance. The Klingons outfitted many ships, particularly their Bird-of-Prey type vessels with the devices.
In 2293 the Klingons tested an experimental Bird-of-Prey that could operate its weapons while cloaked. Captain Kirk of the U.S.S. Enterprise NCC-1701-A and his crew were able to improvise a method to track the ship, eliminating the tactical edge that the Klingon ship would have otherwise enjoyed in starship combat.