This word comes to us through Latin from the Greek khilias “a thousand years”, from khilioi “a thousand”.
It appeared in the English language in the seventeenth century to refer to the belief of some Christian sects that there will come a time when Christ will reign in person on earth for a thousand years, either before or after the Second Coming. So it’s just a more highbrow and less common equivalent of millenarian. But it doesn’t seem to have quite the same figurative sense of belief in a future golden age of prosperity, peace and justice (perhaps an unconscious link with chill is coming into play).
It’s sometimes employed at the moment to refer to the impending millennium in the purely calendrical sense, without any reference to Christian belief, a weakening of meaning that’s similar to the way that millennium itself is so frequently employed.
Malcolm Bradbury recently used it in a review in the Independent on Sunday of Salman Rushdie’s The Ground Beneath Her Feet: “It’s also rich on eschatology, joining all those big-theme novels that have taken the millennial shaking of the world, the sense of historical transition, the collapse of old orders, the signs of apocalypse, the tug of the underworld, as the stuff of timely chiliastic fiction”.