http://www.richimag.co.uk/chickenoregg/
The nesting site is still continually used by gyrfalcons, the world's largest species of falcon, and is the oldest raptor nest ever recorded.
Three other nests, each over 1,000 years old, have also been found, one of which contains feathers from a bird that lived more than 600 years ago.
However, ornithologists fear climate change may soon drive the birds from these ancient nesting sites.
Gyrfalcons live circumpolar to the Arctic. The birds range in colour from being almost exclusively white in Greenland to usually black in Labrador in Canada.
Like many falcons, they do not build nests out of sticks and twigs, but typically lay eggs in bowl-shaped depressions they scrape into existing ledges or old nests made by other birds such as ravens.
But while stick nests are often frequently damaged, preventing their repeated use, gyrfalcons will often revisit some ledges and potholes from year to year.
To find out just how long the birds return to the same site, ornithologist Kurt Burnham of the University of Oxford, UK and colleagues decided to carbon date the guano and other debris that birds leave at various nest sites around Greenland.
The cold dry climate of Greenland slows the decay of the falcons' droppings and various nest sites had built up levels of guano almost 2m deep.
But Burnham was still surprised to find out just how old these nests are.
Carbon dating revealed that one nest in Kangerlussuaq in central-west Greenland is between 2,360 and 2,740 years old, the researchers report in Ibis.
Three other nests in the area are older than 1,000 years, with the youngest nest site first being occupied 520 to 650 years ago.
These ancient nests are still being regularly used by gyrfalcons.
"While I know many falcon species re-use nest sites year after year, I never imagined we would be talking about nests that have been used on and off for over 2,000 years," says Burnham.
Within the nests, Burnham's team also found intriguing clues as to the past inhabitants.
In the 13 nests sampled, they found three feathers belonging to previous tenants. The youngest came from a bird residing in the nest 60 years ago, while the oldest came from a falcon that used the nest some 670 years ago.
The ancient guano samples also gave an indication of what the birds ate in times long past.
Falcons living further north closer to the ice fed on terrestrial prey such as rock ptarmigan and arctic hare.
"These findings put new emphasis on just how important nest site characteristics can be for raptor species, particularly large raptors," Burnham says.
"Something, be it nest ledge depth, or the amount of cliff overhang above the nest, is so attractive at these locations that gyrfalcons are re-using them for thousands of years."
Yet the fact that gyrfalcons remain faithful to certain nest sites for hundreds of generations suggest that they may be especially vulnerable to climate change, says Burnham.
"As a result of a warming and ameliorating climate other bird species, such as peregrine falcons, are moving further north."
"As peregrine populations continue to increase in density they will likely use more and more of these traditional gyrfalcon nests, forcing gyrfalcons to find alternate locations to nest in which may not offer the same amount of protection from the harsh Arctic environment in Greenland."
Similar studies have been used to show when whole colonies of birds first took up residence at certain sites.
By carbon dating solidified stomach contents, peat moss deposits and bone and feather samples from various moulting sites, researchers have in the past shown that colonies of snow petrel have returned to the same sites for 34,000 years and adelie penguins for 44,000 years.
