The Lord Advocate, Frank Mulholland, QC, has appealed to the High Court for authority after changes to double jeopardy laws to set aside the acquittal of Ronnie Coulter, Andrew Coulter and David Montgomery and prosecute them again.
They were acquitted of murder after two separate trials in 1999 and 2000.
The 32-year-old was stabbed to death outside the home he shared with his girlfriend in Overtown in 1998.
The case sparked controversy after an inquiry made allegations of institutional racism.
It marks only the second application to be made through the changes to the double jeopardy legislation.
An accused person can now be tried for the same offence more than once.
The Crown's appeal court application is expected to be heard by the end of the year, while any retrial would not be expected until 2015.
The Crown's move came as Mr Chhokar's family met Scotland's top law officer to discuss new developments in the 15-year-old cold case.
Mr Chhokar's parents Darshan Singh Chhokar and Gurdev Kaur, along with sister Manjit Sangha, joined family solicitor Aamer Anwar for the meeting with Lord Advocate Frank Mulholland, QC, and Solicitor General Lesley Thompson, QC, in Glasgow.
Mr Anwar said: "The Chhokar family is grateful to the Crown Office and Police Scotland for their determination and support.
"Today is an important step but the Chhokar family will only ever be at peace when there is justice."
There were criticisms made of the way the Crown Office prosecuted the accused in two separate trials, a move that ultimately allowed the men to blame each other for the murder.
Ronnie Coulter, who stood accused in the first court case, was convicted of assault, with his nephew Andrew Coulter and his co-accused David Montgomery walking free from court following the second trial.
Two official inquiries were ordered in the wake of the original trial, with one alleging institutional racism within the police and prosecution service, leading to the Chhokar case being dubbed "Scotland's Stephen Lawrence".
Following the publication of the reports in 2001, the then Lord Advocate, Colin Boyd, QC, said the Chhokar family had been failed by the police and prosecution services.
In January 2013, the Crown Office ordered a new investigation into the case and refused to disclose the grounds around which it was prompted.
Prosecutors now say they have new evidence with which to mount a third prosecution.
The recent legislation set out five new conditions on which an accused can be retried for a crime they were previously acquitted of.
They include interference or intimidation of a juror or a witness, a new or previously undiscovered confession, or the availability of new evidence.
The High Court must grant the authority for any fresh prosecution under the Act.
The first application under the November 2011 changes to the double jeopardy laws was made by the Lord Advocate to have Angus Sinclair retried for the World's End murders of Christine Eadie and Helen Scott.
The court on March 27 granted the application, setting aside the acquittals and granted authority to re-indict Angus Sinclair for the murders.
The bodies of Christine Eadie and Helen Scott were found in East Lothian in October 1977.
Mr Sinclair stood trial for their murders seven years ago, but the judge said there was no case to answer.
Before their deaths, Ms Eadie and Ms Scott had been seen at the World's End Pub in Edinburgh's Royal Mile.
The mother of Ronnie Coulter, who was cleared of the waiter's murder, was attacked in her home in 2012.
Three men were jailed in December 2012 for the attempted murder of Mary Coulter, who was 76 at the time.