For a clear, concise history of the Chestnut you cannot beat the well researched and erudite "Oxford Companion to Food" - edited by Alan Davidson, the most readable food historian today:

"The European Chestnut, despite its name, is of W. Asian origin. Around 300 BC the Greek writer Xenophon described how the children of Persian nobles were fed on Chestnuts to fatten them; and it was the Greeks who brought the tree to Europe, from Sardis in Asia Minor. But it flourished more in S. Europe than in its region of origin and deserved the name European long before this came into common use. The more specific name ‘Spanish Chestnut’ probably arose because the best chestnuts imported into Britain came from Spain.
The Romans had the tree in regular cultivation by 37 BC, when Virgil described it in his Eclogues. The Latin name, from which came the botanical name and modern European names, was bestowed on it for the town Castanea in Magnesia (now Central Turkey), where the tree was especially common. The Romans made Chestnuts into flour, which was used to extend wheat flour, a practise which survives in S Europe. Apicius (the only classical cookery book, surviving from the Roman Empire) gave a recipe for Chestnuts cooked with lentils. The Romans also took the tree north, to Gaul and then to Britain.