Mr Ashdown, on a fact- finding mission to the province, the latest of many trips to the Balkans, said: "The situation now in Kosovo is a race between order and disorder and disorder has a head start."
Speaking from the capital, Pristina, he said: "The world probably believes that there is a humanitarian crisis in Kosovo - there is a humanitarian challenge but I'm reasonably convinced that it will get through the winter. There isn't a humanitarian crisis, but there is an administrative crisis and unless we tackle that there is a danger that Kosovo will simply descend into Balkan chaos."
Mr Ashdown's remarks reflect growing fears that the international forces running Kosovo are failing to keep the province under control. Every day, Serbs are driven out of their homes by Albanians who have returned to rule the roost. Meanwhile, Albanians settle scores among themselves.
Slobodan Milosevic's Serb-run police are gone; the only Albanian force that could replace it is the Kosovo Liberation Army, whose supporters include a heavy sprinkling of thugs.
Kosovo Serbs are so frightened that most have fled. Those who stay are deeply scared. Nor is this just ethnic revenge. Criminals from Albania and from Kosovo itself have the run of the unpoliced province.
For this problem to be fully addressed, the now powerful KLA, with all its murky connections, will need to have its wings clipped. But it will be difficult to bring under control a force that Kosovo Albanians are more loyal to than ever before.