Hain is a fictional planet that plays an important background role in the science fiction novels of Ursula K. Le Guin's Hainish Cycle. It is described more closely in some later short stories. It is the oldest culture in both the League of Worlds and later the Ekumen and is about 140 Light Years from Terra/Earth . Observers like Genly Ai in The Left Hand of Darkness are trained on Hain.
Hain is also known as Davenant or Hain-Davenant. Its people cannot readily be distinguished from Earth-humans, but they have evolved differences, including the ability not to conceive children or father them without a conscious decision to do so.  It once had a high-technology culture, and also seeded humans or humanoids on various planets, including Earth and other worlds now in the Ekumen. Exact details are no longer known, but the history of the people of Hain goes back three million years.  Knowledge has mostly not been lost, but is used more wisely.
The 'Ekumen' is very loosely knit, with Hain at the centre but not ruling. The Hainish attitude was different during the "vast Hainish expansion of the Fore-Eras". It is mentioned in The Left Hand of Darkness that the original Hainish culture probably created the Gethenians as an experiment.
From the older high-tech culture there was a crash and a re-building on a wiser basis. Evidence of the former high-tech life is all around, along with proof of the current indifference to it:
Three of the short stories in A Fisherman of the Inland Sea include details of life on Hain. More is seen in the first half of A Man of the People in Four Ways to Forgiveness. Havzhiva is a man who grows up on Hain, though he ends up working for the Hainish embassy on Yeowe. We see the ruins of past technology and learn of the highly localised social order that exists on some parts of the planet.