Wildlife enthusiasts had been watching the chicks and their mother and last saw them on the evening of 27 May.
However all of the birds, which can be sold for thousands of pounds, disappeared from their Sutton Bank nest in the North York Moors before 4 June.
North Yorkshire Police is investigating whether the disappearance was because of a predator or a criminal act.

NUS lawyers have written to Business Secretary Sajid Javid, demanding he properly considers the equality impact of the move.
Plans to scrap grants were announced by Chancellor George Osborne in his budget in July.
The government said it would respond to the letter in due course.
Currently, students whose family income is below £25,000 are eligible for full grants worth up to £3,387 plus a loan of £4,047 if they live away from home outside London.
Partial grants on a sliding scale are available for students whose family income is below £60,000.
The government wants to replace the grants with loans for new students from next year.
In its judicial review pre-action letter, the NUS identifies "a serious and unlawful failure" in the government to discharge a duty set out in the 2010 Equality Act to consider the impact of the policy on the poorest students.
"The abolition of maintenance grants will cause a very significant increase in debt for the poorest students; from £40,500 to around £53,000 at a time when the impacts of the 2012 recent reforms remain to be properly analysed and understood," says the letter.
NUS President Megan Dunn called the government's plan "reckless", citing "strong evidence" the change would mean higher education "becomes less accessible to minority groups".
She added: "We know the huge damage that this change will have if it is allowed to happen. It is obvious that the government is attempting to rush through these changes with no consideration on future generations of students."
Salima Budhani of legal firm Bindmans said the NUS was calling upon the secretary of state "to halt plans to abolish maintenance grants and to gather information to enable him to properly consider the complex equality considerations at stake.
"An open minded reconsideration of the policy should then take place."
A spokeswoman for the Department for Business Innovation and Skills said students would not have to pay back anything until their earnings rose above £21,000.
The maintenance loan for all students would also rise from next year to £8,200 for students living away from home outside London: "the highest amount of support ever provided", the spokeswoman added.

The 21-month-old from Sheffield, South Yorkshire, went missing during a family holiday in July 1991.
A fresh excavation of farmland began on Monday, following new evidence that he may have been killed and buried there.
Police said they found "a vast number" of animal bones and small pieces of fabric which were "of slight interest".
A 19-strong team of South Yorkshire Police officers, forensic specialists and an archaeologist have been scouring the arid stretch of olive grove, which has been used for farming for generations.
More on this story and more on BBC Local Live: Sheffield and South Yorkshire
Ben was last seen playing on the land and it is close to where he vanished while his grandfather was renovating a property 25 years ago.
His family believe he was abducted, but police are now investigating whether he was accidentally run over and killed by a bulldozer.
Det Insp Jon Cousins, from South Yorkshire Police, said the team - joined by local search and rescue volunteers - had made good progress in recovering potential evidence.
He said: "We found, as expected, a vast number of bones yesterday. Each one was examined immediately, and each one was discounted there and then as being an animal bone.
"There are some other items that are of slight interest - the odd piece of fabric. That is being analysed and looked at, but there is slight interest.
"Everything is being carefully looked at."
He added: "We want to make sure: do they or do they not relate to any of the items Ben was wearing on that day?"
On the day Ben went missing he was wearing a white and green shirt and a pair of leather sandals.
The recovered items have been forensically collected and photographs sent to colleagues back in the UK before a decision is made on whether they require further examination and testing.
The search is expected to last about a week.
Three peregrine falcon chicks have gone missing from a nest in North Yorkshire, sparking a police investigation.
[NEXT_CONCEPT]
The National Union of Students (NUS) has taken the first step in legal action over government plans to scrap maintenance grants in England.
[NEXT_CONCEPT]
Police searching for missing toddler Ben Needham on the Greek island of Kos have found pieces of fabric on land close to where he was last seen.