The historic Lewis chessmen could be housed in an extension of the British Museum built on the Western Isles, the islands SNP MP has suggested.
Angus MacNeil told a debate in Westminster that most, if not all, the 93 pieces should be returned to Lewis where they were found buried in 1831.
UK Culture Minister Margaret Hodge said keeping them in London allowed many people to share in their history.
Eleven of the chessmen are held by the National Museum of Scotland.
Mr MacNeil said moving the pieces to Lewis would have a "measureable" benefit for the islands, but only a marginal loss effect on the British Museum.
When a fellow MP's mobile phone rang during the debate, Mr MacNeil joked that it was the museum calling to say the chessmen would be returned to Lewis.
Mr MacNeil also said he was open to a suggestion from an English MP that what have been claimed to be the remains of King Richard II found buried at Stirling should be returned to England.
Earlier, the islands MP said it was wrong that a poster for a joint BBC and British Museum project showing the historic Lewis chessmen said they were made in Norway.
Mr MacNeil said a theory they were carved in the Scandinavian country had not been confirmed.
The British Museum said it was generally accepted the pieces were made in Norway.
The poster promotes the BBC Radio 4 History of the World in 100 Objects series, which is running in partnership with the British Museum.
Mr MacNeil said he spotted the poster in London Tube stations.
He told the BBC's Good Morning Scotland programme: "We only know two real things about the Lewis chessmen prior to 1831.
"They were made from walrus ivory, or whale teeth, and they were buried on Lewis for hundreds of years.
"They might well have been made in Norway, but they might well have been made in Lewis and there are some who say the carvings on the side of them would place them on Lewis."
The British Museum said a museum on the Western Isles had helped with the world history project.
A spokeswoman said: "It is generally accepted that the chessmen were made in Norway, during this period the Western Isles, where the chessmen were buried, were part of the kingdom of Norway not Scotland.
"The British Museum is delighted that Museum nan Eilean in Stornoway is enthusiastically contributing to the A History of the World project.
"The British Museum is also working with the National Museums of Scotland on a tour of a group of the chessmen to four venues across Scotland in 2010-11."