Many chess historians believe that chess started in India near the end of the 6th century A.D. Afterwards it slowly migrated to Persia, then to the Arab world, then to Europe. Some historians believe that chess originated in China, although they are in the minority.
The origin of chess theories are largely based on a few literary references which have survived to our day. Controversies arise because its not always clear that the references are to chess or to another game. Real physical evidence one way or the other is missing.