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Lindy Chamberlain, who is seven months pregnant, is accused of slitting Azaria's throat as she sat in the front seat of the family car at a campsite at Ayers Rock.
The mystery of Azaria's disappearance two years ago attracted widespread publicity. Her body has never been found.
The original inquest into the baby's death found she had been killed by a dingo, but new forensic evidence led to a second inquest which suggested the child's throat had been cut and Mrs Chamberlain was sent for trial.
Her husband Michael, a Seventh Day Adventist minister, is also on trial, accused of trying to cover up the truth.
Mr and Mrs Chamberlain have both pleaded not guilty.
The courtroom was packed for the first day of what has already been dubbed by one newspaper as Australia's "trial of the century".
Prosecutor Ian Barker told the court Mrs Chamberlain's story that her baby had been taken from the couple's tent by a dingo was a "fanciful lie to conceal the truth".
Neither of the accused showed any emotion as the bloodstained jumpsuit worn by Azaria at the time of her disappearance was exhibited to the courtroom.
Mr Barker told the court extensive tests by a team in London would convince the jury the baby's throat had been cut, not savaged by a dingo.
He said traces of blood had also been found in the family car more than a year after Azaria disappeared.
Tests showed attempts had been made to wipe away the blood. Further investigations revealed the blood came from a child less than six months old, suggesting it was Azaria's.
He continued the tiny amount of blood found in the Chamberlains' tent was inconsistent with a dingo attack. Nor were there any traces of saliva found on the baby's clothing which would have supported the claim.
The child's clothing was found close to a dingo's lair, seven days after her disappearance. The prosecution claimed it had been planted there after the child's body had been buried.
Mr Barker said he would not suggest a motive for the killing, nor would he suggest Mr Chamberlain had been involved - but he probably learned about it soon afterwards and helped conceal the truth.
The trial is scheduled to last more than six weeks and should end just before Mrs Chamberlain is due to give birth, early in November.
Lindy Chamberlain was found guilty of murdering her daughter and her husband Michael of being an accessory. She was sentenced to life in prison with hard labour. He was given an 18 month sentence which was suspended for three years.
The case sent shockwaves around the world. Lindy Chamberlain's sentence was seen as very harsh and even senior legal experts in Australia questioned whether she had been found guilty beyond reasonable doubt.
The case had barely finished when two books were written about it and a film planned.
Lindy Chamberlain appealed against her conviction and lost. But then in 1986 a matinee jacket belonging to baby Azaria was found close to a dingo's lair at Ayer's Rock.
Mrs Chamberlain was released five days later on the grounds "she had suffered enough".
The Chamberlains were pardoned in 1988. A further inquest in 1995 returned an open verdict.
In July 2004 a man came forward saying he shot the dingo carrying baby Azaria but did not tell anyone for fear he would be prosecuted. He said one of his friends buried the child's body.
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