It is the first one of which we have a detailed historical account (by the historian Thucydides). It occurred 431-404 BCE.
Of course wars had been going of for thousands of years before that - we have fragmentary accounts of wars in Egypt, Mesopotamia and China for the two millennia before that, and there is no reason to believe that there were earlier conflicts, as archaeologs has unearthed ruined towns from thousands of years earlier.