What caused the original 'thousand year war' between the Kree and the Xandarians?
The short answer is, we have no idea.
Marvel Cinematic Universe
The Guardians of The Galaxy movie never goes into any detail about the origins of the war. At the start of the movie, the war has "been going on" for a long time. Indeed, the Nova Corps on Xandar was formed largely to defend Xandar from the Kree. (This is why their crafts are so well equipped to counter Ronan's vessel near the end.)
As far as I know, there was never anything like a Kree/Xandarian war in the mainstream Marvel continuity. The closest I could find was an instance where the Nova Corps became involved in a war between the Kree and the Shi'ar.
In the comics, the main enemy of the Kree race are the Skrull, with the Kree-Skrull War taking up quite a lot of space in the Avengers comics.
There is some history between the Guardians of the Galaxy and the Kree; the origin story from Earth-616 has the Guardians forming to fight off the Kree invasion of a star system, just not the one Xandar is in.
(I can speculate that Nova Corps just made a convenient "clearly-the-good-guys" space faring group to put into the Guardian's origin story, that was slightly less bizarre that Cosmo the talking dog. So they invented the war to give Ronan an excuse to be mad at Xandar and kick-start the story.)
I'm unaware of any specific reason mentioned in the film to describe why the Kree and the Nova Empire went to war for however the Kree are described on the Marvel Wiki as extremely aggressive and expansionist, having existed in a state of near-constant warfare with their neighbours (including the largely peaceful Skrulls) for hundreds of millennia.
The Kree launched an attack upon the Skrull empire and the peaceful Skrulls were again forced to become war-like to defend themselves. The Kree-Skrull War would continue for hundreds of thousands of years.
The best guess would be that the Nova Empire are merely the latest in a long line of victims of their enmity.