The Klingons are a proud warrior race but, amusingly, their greatest enemies in Tribbles. In their centuries as both adversaries and allies of the United Federation of Planets, the Klingon Empire fought many wars and conquered numerous races but their very survival was once severely threatened by the soft, furry, mindless creatures introduced in the classic Star Trek: The Original Series episode, "The Trouble With Tribbles".
Both the crew of Captain Spock (Leonard Nimoy) calculated that the average Tribble produced a litter of 10 every 12 hours, which would for a single Tribble being able to create 1,771,561 progeny in the course of three days. At the end of the episode, the crew of the Enterprise beamed the Tribbles that infested their ship to the Klingon vessel commanded by Koloth (William Campbell) and all's well that ended well for Kirk's starship - but not for the Klingons. Ironically, Tribbles are affectionate towards humans but they are hostile towards Klingons - and the feelings are mutual.
The Worf (Michael Dorn), after the encounter between Kirk and Koloth, the Tribbles were declared mortal enemies of the Klingon Empire. The Tribble population infested the Klingons and became an ecological menace that had to be wiped out. Not only were hundreds of Klingon warriors sent to track down and destroy Tribbles throughout the galaxy but a Klingon armada obliterated the Tribble homeworld. This s for why the Tribbles were nearly extinct by the 24th century - until Sisko's crew inadvertently brought a swarm of Tribbles back with them, which briefly took over their space station, Deep Space Nine.
It's a ridiculous thought that the mighty and savage Klingons were so fearful of otherwise harmless balls of fur that they went to war with the Tribbles and even committed genocide. Constable Odo (Rene Auberjonois) even mocked Worf at the very idea of this "glorious chapter in Klingon history" and asked, tongue-in-cheek, if the Klingons "still sing songs of the great Tribble hunt"? But Trekkers in the know truly understand what a scourge Tribbles can be and, even though Star Trek's Tribble episodes are refreshingly comedic, the underlying ecological crisis they pose is no joke.
The Tribbles have been retconned so that they appeared in the prequel series Star Trek: Enterprise and in Short Trek episode, "The Trouble With Edward", revealed that years before Kirk encountered the Tribbles on K-7, an idiot named Edward Larkin (H. Jon Benjamin) experimented on Tribbles as a food source. Larkin infused them with his own human DNA, which is what caused the Tribbles' reproductive rate to increase. The Tribble population immediately multiplied and led to the destruction of the scientific vessel, the U.S.S. Cabot. Some hybrid Tribbles survived the Cabot and landed on the planet Pragine 63, which led to that world being evacuated before the Tribbles later made their way into Klingon space.
So, despite the bloody conflicts the Klingons waged against the Federation and the Cardassians, the Tribbles are the only known time the warrior race was forced to commit genocide to save themselves. Even the Dominion, which nearly conquered the Alpha Quadrant in Star Trek: Deep Space Nine, didn't pose the kind of existential threat to the Klingons that the Tribbles did. And while the Klingons normally boast about their glorious battles, they're understandably reticent to discuss the lengths they went to in order to defeat the Tribbles, which they would be ashamed to it were their greatest enemies.