The Odyssey, attributed to Homer, is commonly dated to around 800 BC, written on the author's home Iona, now the oceanside coast of Turkey.
Interestingly, there are some who feel that the story actually comes from around 1170. That's almost 400 years older than previously thought. They have used a computer to analyze astronomical data from the general time period and to try to match it with clues from the story:
"The first clue is Odysseus's sighting of Venus just before dawn as he arrives on Ithaca. The second is a new moon on the night before the massacre of the suitors. The final clue is a total eclipse, falling over Ithaca around noon, when Penelope's suitors sit down for their noon meal. The seer Theoclymenus approaches the suitors and foretells their death, saying, 'The Sun has been obliterated from the sky, and an unlucky darkness invades the world.'"
They used computer software to scan the positions of all 1684 new moons during that general time period for dates that match all of the evidence, an occurrence that doesn't happen very often. This is how they came up with the year 1178. This actually kind of corresponds with another event in the book, the fall of Troy, which archaeological evidence suggests was about 1190 (putting it at just about the right time frame for Homer's story.) Anthropologists hadn't thought the Greeks were well versed at astronomy during this time, but these findings show that Homer must have understood a lot about the stars to include them in his story.