There was a time today when it was 1 second, 2 minutes, 3 hours, 4 days, 5 months, and 6 years into the new millennium. Counting time can be done in different ways. Danny Hillis wants "to build a clock that ticks once a year. The century hand advances once every one hundred years, and the cuckoo comes out on the millennium. I want the cuckoo to come out every millennium for the next 10,000 years. If I hurry I should finish the clock in time to see the cuckoo come out for the first time."
Wired magazine featured Danny's idea more than eight years ago and a prototype was built that chimed in the new millenium on New Years Eve, 1999. Steward Brand has an article about choosing where to locate the clock and Wikipedia has an entry, "Clock of the Long Now". Discover magazine has more coverage and some great photos of the "Long Now" clock.