The former Governor of New Jersey Jim McGreevey and his estranged wife Dina have failed to come to a settlement and their divorce case is due to begin today.

They reached a deal on the custody of their only child, six-year-old Jacqueline, last week, the details of which are sealed by court order.

Mrs Matos McGreevey is seeking an additional settlement, claiming marriage fraud.

Her husband became America’s first openly gay Governor when he came out at a televised press conference four years ago, telling reporters : “My truth is that I am a gay American.”

He made a dramatic public confession of an affair with his former homeland security advisor, Golan Cipel and left office two months later, in November 2004.

His wife is claiming she was tricked into marrying a gay man in order to further his political career.

Despite standing by her husband when he came out, their separation and divorce has been one of the most vicious in recent memory.

The former Governor wrote a memoir, The Confession, and appeared on Oprah last year.

He shocked viewers with his confession of an encounter with a gay aide while his wife lay in bed in hospital following the difficult birth of their child.

He now lives with his boyfriend, Australian business executive Mark O’Donnell, and is training to be an Anglican priest.

A Roman Catholic while Governor, Mr MrGreevey has been attending Anglican services since 2004.

He has been accepted into a masters degree programme at the General Theological Seminary but it is several years before he would be considered for ordination.

Dina Matos Mc Greevey’s book, Silent Partner, came out earlier this year. She also appeared on Oprah.

Following the former Governor’s admissions, and further revelations of sexual encounters at highway rest stops, Mr McGreevey and his second wife began divorce proceedings.

In March a judge ruled that he didn’t plan on tormenting his wife while married.

Judge Karen Cassidy said: “Mr McGreevey was not out to destroy her emotionally.”

But she said that Mrs Matos McGreevey could continue with her claim of fraud against her husband but warned: “That does not guarantee the defendant will be successful in trying her claim.”

Former McGreevey driver, Teddy Pedersen has claimed he engaged in a consensual threesomes with the couple two years before Mr McGreevey became Governor.

Mrs Matos McGreevey said that was untrue but her husband admitted to the sexual encounters.

His estranged wife also rejected the claims by their former driver that she was aware that her husband was gay when she married him.

Pedersen told the Newark Star-Ledger that he had sex with Dina Matos McGreevey while her husband watched at the couple’s condo in Woodridge, N.J.

The sex often took place after dinner at a local T.G.I. Friday’s, he said.

In an email to ABCNews.com, she claimed that McGreevey had set up Pedersen, one of his “cronies,” to spread the tale because her former husband “cannot stand it when I am receiving attention in the media rather than him.”

Pedersen has filed a sworn deposition as part of the McGreevey’s brawling divorce proceedings that the three of them frequently engaged in what they called “Friday Night Specials.”

The encounters reportedly stopped before McGreevey became Governor. His lawyer intends to present Pedersen as a witness in the divorce case.