She successfully acted for the council on several high-profile Treaty of Waitangi claims against the Crown in the late 1980s through to the mid-1990s.
Some Cabinet ministers take the view that because of this strong and lengthy relationship as one of the council's prime legal advocates, she should recuse herself from the upcoming appeal by the Maori Council against High Court judge Ron Young's judgment effectively clearing the way for the Government to sell down its shareholding in Mighty River Power.
At first blush it would seem unlikely Elias would take this step.
Lawyer Stephen Franks was criticised after he said in Parliament that the Chief Justice should have recused herself on the Ngati Apa case that "plunged us into the seabed and foreshore mire" . In 2005, Franks argued that New Zealand needs a mechanism to neutralise the suspicions that will attend such judges in areas of passion.
"We need access in some cases to patently impartial international umpires, outside the cosy hot-house that is our senior legal society," Franks said, noting that it is no solution to say that we should not appoint judges like Dame Sian.
"We do not want only judges who have been so incurious or toadyish or colourless or spineless as to have never participated in the great debates of our society."
But there have been few others who have dared to publicly question her role in presiding on such cases.
When Elias has stood aside it has been when a direct personal conflict has arisen. For instance, when she scratched herself from a Supreme Court case involving jockey Lisa Cropp who had been riding one of the judge's horses. There were also criticisms over the Supreme Court's handling of the Bill Wilson affair.
The Chief Justice made her name in the pivotal 1987 case where the late Justice Sir Robin Cooke handed down a Court of Appeal ruling in the Maori Council's favour establishing a key principle of the Treaty of Waitangi as "partnership". Elias - with David Baragwanath - acted for the council.
The water rights case will go straight to the Supreme Court for a full-court hearing on January 31. The single ground for appeal is whether Young was right to dismiss the council's application to review the Government's decisions on the sell down of Mighty River Power because of outstanding claims to water rights.
At Government level there is also concern over the very legitimacy of the Maori Council.
Cabinet ministers such as Bill English - who was second respondent in the council's High Court action - are sceptical over the council's standing.
He contends that it doesn't really represent the Maori leadership of today. But it would be surprising if the Government tried to reopen this issue at Supreme Court level.
The asset sales are a major part of the Government's fiscal programme. If it can release the multibillion-dollar revenue from the three energy companies it will resolve a difficult Budget hole.
If the Supreme Court rules against the Government the stakes will be heightened. But if the Supreme Court, - with Elias at the helm - did uphold Young's judgment, the Government would be in a very strong place indeed.
Big calls all round and plenty of soul-searching over Christmas.
