Millennium

n.
  1. A period of one thousand years.
  2. A thousandth anniversary;

Technically, if the calendar of the Common Era (Anno Domini) is considered as beginning on January 1, 1 a. d., then the millenium will fall in each year ending in 001, as in 1001 a. d. or January 1, 2001 a. d.. However in the common culture, the change of the first digit of the year from 1 to 2, as from 1999 to 2000 is considered as the more symbolic event, especially since the dating of the beginning of the Christian era is somewhat arbitrary, having been an attempt to fix the date of the birth of Christ, and being considered by scholars as being in error by as much as five years.