Mr Chhokar, 32, was stabbed to death outside the home he shared with his girlfriend in Overtown, Lanarkshire, in 1998. The case was dubbed “Scotland’s Stephen Lawrence” amid claims of “institutional police racism”.
Ronnie Coulter, his nephew Andrew Coulter and David Montgomery were acquitted of murder after two separate trials in 1999 and 2000.
Now Lord Advocate Frank Mulholland has applied to the High Court to have their acquittals set aside in order to bring a fresh prosecution.
The case is the second application to be made under the Double Jeopardy (Scotland) Act 2011, which allows acquitted suspects to be tried again.
Last month, the Crown Office said an application had been granted allowing the retrial of Angus Sinclair, who was acquitted of the notorious World’s End murders of 17-year-olds Christine Eadie and Helen Scott in 1977.
The Chhokar family’s solicitor, Aamer Anwar, said his clients would only “be at peace when there is justice”.
He said: “In January 2012, following the conviction of two men for the murder of Stephen Lawrence and the subsequent reform of the double jeopardy law in Scotland, I requested that the murder case of Surjit Singh Chhokar be reopened by Police Scotland.
“It was confirmed at a meeting between the Chhokar family and the Lord Advocate and the Solicitor General that the police would be asked to conduct a fresh investigation into the murder. There still remain significant legal hurdles to be overcome.
“Fifteen long years after Surjit was murdered, people may have forgotten his name but his family never gave up hope for justice.
“The Chhokar family are 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.”
A statement from the Crown Office said: “The Lord Advocate, Frank Mulholland QC, has today applied to the High Court for authority under the Double Jeopardy (Scotland) Act 2011 to set aside the acquittal of Ronnie Coulter, Andrew Coulter and David Montgomery, and prosecute them again for the murder of Surjit Singh Chhokar.”
Two official inquiries were ordered in the wake of the original trials. One of them made allegations of “institutional racism”, echoing Sir William MacPherson’s inquiry into the Metropolitan Police’s handling of the murder of black teenager Stephen Lawrence in south London in 1993.
Following the publication of the Scottish reports in 2001, the then lord advocate, Colin Boyd, said the Chhokar family had been failed by the police and prosecution services.
In 2012, police said they had been instructed by the Crown Office to carry out a new investigation into the unsolved murder of Mr Chhokar.
The victim’s family had met prosecutors before they instructed police to reinvestigate the case two years ago.
In March, the Crown was granted permission to bring a fresh prosecution against Sinclair for the murders of Christine Scott and Helen Eadie.
The bodies of the girls were found in East Lothian in October 1977 after they were last seen at the World’s End Pub in Edinburgh’s Royal Mile.
That retrial would be the first after double jeopardy legislation changed in November 2011. Until the new legislation was introduced, people could not be retried for the same crime.