One of the blogs I visit regularly is God of Wednesday. Nancy Marie Brown's blog about Iceland - the horses, the landscape and the history and folklore. Just recently she's been talking about the book she's written called Ivory Vikings, in which she considers the history of the Lewis chessmen in relation to Iceland.
Her theory is that the chessmen were carved on Iceland, which was certainly a source of walrus ivory, by Margaret the Adroit, hailed as the best carver in Iceland in the Saga of Bishop Pall. She was a member of his household.
The idea that Iceland was the source of the chessmen had been written off by earlier scholars, who had the idea that Iceland was a poor backwater, incapable of producing artists of the calibre of the carver of the chessmen, and too poor to afford the large amount of walrus ivory that went into the pieces. However, Nancy Marie Brown argues that Iceland was going through a Golden Age at this time, and Bishop Pall was wealthy, well-educated nobleman, with several artists in his retinue, including Margaret.
To me, this seems the best theory that's been put forward so far.