The current way of dealing with the past in NI is a "huge money-sucking venture", Sir Hugh Orde said.
Sir Hugh Orde is concerned at the amount of money being spent on inquiries
The chief constable said he understood £18.5m had so far be spent on inquiries into the killings of Rosemary Nelson, Billy Wright and Robert Hamill.
"Unless I have missed it, there has not been a day's hearing in those" he said.
"I think dealing with the past in the current way is a huge money-sucking venture because it deals with these people called lawyers."
He added: "History needs dealing with. The Bloody Sunday inquiry is nearly 10 years old now and that is nearly £180m.
"So the way we are dealing with it currently, it is hugely expensive and that is clearly two police colleges and a hospital."
Sir Hugh said that the PSNI's Historical Enquiries Team, which was set up to investigate killings carried out during the Troubles, was another way to deal with the past.
"What we are finding is where people are engaging with us we are getting positive feedback from families who are learning a lot more now than they ever did," he said.
"Again it shows the families of the victims are ahead of the politicians. They are not playing games with this.
"They want to know what happened and many are not interested in prosecution. They just want to know the story."
The chief constable also said it would be tragic if the new police training college - a recommendation of the Patten report - was not built because of a lack of funding.
"It was one of the jewels in the Patten crown because it was one of the things which defined police excellence worldwide in the next 20 to 30 years," Sir Hugh said.
"Against that backdrop it does seem remarkable that we cannot find a few extra million pounds to make a world-class training establishment where people will come to learn from our experiences as opposed to the other way round."