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One of the most common ways for chess historians to trace when the board game chess entered a country is to look at the literature of that country. Although due to the names associated with chess sometimes being used for more than one game (for instance Xiang-qi in China and Tables in England), the only certain reference to chess is often several hundred years later than uncertain earlier references.
The earliest dates for strong references include,
a. 923 AD - at-Tabari's Kitab akhbar ar-rusul wal-muluk (note the work is an arabic work, no early greek works are known)
c. 900 AD - Huan Kwai Lu ('Book of Marvels')
c. 1180 AD - Alexander Neckam's De Natura Rerum (note that it is thought that Neckam may have learnt of chess in Italy, not in England)
a. 1127 AD - A song of Guilhem IX Count of Poitiers and Duke of Aquitaine.
c. 1070 AD - Ruodlieb thought to be written by a monk near Tegernesee.
1148 AD - Kalhana's Rajatarangini (translated by MA Stein, 1900)
(note this refers to the old four-handed chess sometime known as chaturagi).
c. 1061 or 1062 AD - Letter from Petrus Damiani (Cardinal Bishop of Ostia) to the Pope-elect Alexander II and the Archdeacon Hildebrand. This letter is dated by the reference to Alexander as "Pope-elect".
c. 600 AD - Karnamak-i-Artakhshatr-i-Papakan
(It is fairly certain chess is meant due to the word chatrang being used).
13th century - Kormchaya Kniga, a set of church laws.
c. 1009 AD - castrensian will of 1620 AD - Sejarah Malayu
c. 997 AD - Versus de scachis in manuscript 319 at Stiftsbibliothek Einsiedeln.