The Chief Constable will arrange an independent investigation into the controversial 1972 death of a Belfast mother before he leaves office.
George Hamilton made the pledge after meeting relatives of Jean Smyth-Campbell yesterday.
The 24-year-old was shot dead while sitting in a car on the Glen Road on June 8, 1972.
Her death was originally blamed on the IRA but the Military Reaction Force, a secretive army unit, was later suspected.
Ms Smyth-Campbell's daughter Sharon McVicker was six years old when her mother died.
She travelled from Australia to meet the Chief Constable over concerns about how the case will be investigated.
The meeting follows the news that the PSNI, Northern Ireland Office (NIO) and Department of Justice (DoJ) are seeking to challenge a Court of Appeal ruling last month.
The court said police lacked the necessary independence to investigate the murder, and the NIO and DoJ did not provide an investigation that complied with European Human Rights law.
Mr Hamilton said yesterday: "I appreciated the opportunity to meet with the family of Jean Smyth-Campbell personally.
"I offered a sincere apology for the failures to bring them justice over the last 47 years.
"Having listened to their views, I have given a commitment to finalise the appropriate mechanisms for practical independence and Terms of Reference before I leave office at the end of June."
Mrs McVicker called the meeting "productive". She said: "If the Chief Constable holds up the recommendations he's made today by (his retirement date) June 30, then we'll have our independent investigation under Article 2 of the European Convention of Human Rights.
"That's what we have requested, that's what the judge has ruled. If he holds that up then I think it was a worthwhile meeting."
After nearly 50 years of uncertainty, she said an independent investigation could finally give the family closure.
"We'll know exactly what happened to my mother. My grandmother died not knowing the circumstances surrounding her death.
"We also want an apology from the people who murdered her, we would love justice and to hold those people accountable, but we're not quite sure that would happen."
Ms Smyth-Campbell's sister Margaret McQuillan said it had been an emotional morning for the family. "We have been through hell and back with this case and when we heard about the appeal we were just deflated, we were angry," she said.
"The Chief Constable has promised the investigation so hopefully that will lift our spirits."
She added: "Jean never leaves the family and hasn't done for 47 years because we always knew there was something not quite right with her murder.
"It only came to light five years ago (that the Military Reaction Force could have been responsible for the shooting) and we'll keep going till we get her justice."
Niall O'Murchu from Kinnear & Co, a legal representative for the Campbell family, said they will assess Mr Hamilton's terms.
"That would mean an investigation that won't involve the PSNI investigating this death. We would just say it's a wait and see process."
While the PSNI are appealing part of the judgment which relates to their independence, the NIO and DoJ are appealing the full judgment.
Mr O'Murchu said: "If they are successful, that would stymie the ability of a future Historical Investigations Unit (HIU) to go about its business, they wouldn't have to investigate to an Article 2 standard."
Belfast-based researcher Ciaran MacAirt first uncovered files that suggested the MRF were involved in the death.
"A lot of families will be watching this case because we realise how significant it is," he said.
"Not only for the family of Jean but also the families of Kelly's Bar and McGurk's Bar, the New Lodge six and many others that might have involved British military or RUC police cover up."