This is the most that David is entitled to under Sir Robert's and Lady Deborah's relationship property agreement.
That agreement said whoever of the couple survived the other may, at their discretion, pay an entitlement to one or both of the deceased's children.
However, it also said that the survivor should be able to "enjoy the parties' relationship property to the full for his or her life" and to defer the payment of any entitlement as long as it was "inflation-proofed".
Ahead of last year's High Court hearing, Lady Deborah had declined David's request for the $2.5 million and said that he was not in financial need.
It was her view she was not required to make a payment at that point and it was not Sir Robert's intention that she do so.
The parties appeared before Justice Jillian Mallon last October, where David attempted to remove Lady Deborah and another administrator from Sir Robert's estate so he could pursue his claim for the $2.5 million.
He also, during that hearing, argued that Lady Deborah held his entitlement as a constructive trustee and further claimed she held it pursuant to an "express trust".
However, Justice Mallon found there were no grounds to replace Lady Deborah and the other administrator under Sir Robert's will.
The judge also said, in her just-released decision, that David's express trust claim did not have merit.
However, the situation was different when it came to the constructive trust argument.
Although she also dismissed this part of David's claim, Justice Mallon said he had enjoyed a "measure of success" with it.
She concluded that Lady Deborah has "fiduciary obligations" when considering whether to exercise her discretion to pay David his entitlement.
While Lady Deborah was permitted to enjoy her and her late husband's relationship property "to the full for the rest of her life", Justice Mallon said this did not "override the requirement to also consider the interests of Sir Robert's sons".
"She is required to exercise her discretion from time to time in light of all the relevant circumstances ... the relevant circumstances include David's wish for a payment now," the judge said.
That discretion, properly exercised, may or may not lead to a payment of some or all of the entitlement, the judge said.
The proper remedy is not therefore to compel a payment of some or all of the entitlement.
Jim Farmer - the Queen's Counsel for David - said his client's request for an "early payment" would now be renewed.
"The judgment has clarified that Lady Chambers is not entitled to take the view, as she has, that David must wait until her death to receive the moneys that his father intended he should have unless he can in the meantime show a financial need for an earlier payment," Farmer said.
"The judge has ruled that Lady Chambers owes fiduciary obligations to David and that she must take account of David's wish that he be paid now," he said.
On the other hand, Julian Miles - the QC for Lady Deborah - said that David had failed in his attempt to require immediate payment of the $2.5 million.
"There is no requirement that David Chambers be paid anything as a result of the judgment," Miles said.
"The position remains that subject to appropriate consideration of his interests, David Chambers will receive his entitlement on the death of Lady Chambers ... Lady Chambers has no difficulty with recognising that she should exercise any powers she has under her husband's will in light of all of the relevant circumstances including David's wish that he receives a payment now. She will be abiding by the decision and is pleased that her husband's will has been upheld despite the challenge by David."
Lady Deborah, in a statement to the Herald, said:
"I am very pleased that my husband's wishes have been upheld by the High Court. We had four children, all of whom we loved very much and we loved each other very much. We had mirror wills and agreements, all drafted by Rob to be fair to all of our family," Lady Deborah said.
"We treated all four of our children equally and we treated ourselves equally in the event of either of our deaths. Only one child, David, considered the arrangements were unfair to him. The litigation has been distressing because of its affect on the family unity Rob and I worked so hard to build and the inevitable publication of our personal lives. I will continue to uphold my husband's wishes and look after the interests of all four of our children," she said.
