The documents also show that Mr Chick claimed to have "influence at the highest political level".
He put money offshore in the British Virgin Islands as part of an employee benefit trust alongside his business partner Jim Davis.
Lawyers for the men said their clients had "paid appropriate tax on all monies earned in the UK".
Much of the money came from their property company Eastonville Traders Limited, with which they are no longer involved.
In 2011, HMRC tightened the rules around bringing money from employee benefit trusts (EBTs) back to the UK - and any money coming back could be liable to a large tax bill.
The Paradise Papers files revealed that Mr Chick and Mr Davis' company, Dunadry Holdings Limited, needed £600,000 to develop a site at Crawfordsburn.
Mr Chick had that money in a company in Mauritius. He wanted it back in the UK, so he sought advice.
That advice sought by Mr Chick's company in Mauritius stated that he could be liable for a 45% income tax bill.
That meant that the £600,000 loan could rack up a bill of £270,000 if HMRC were aware of the original source of some of the funds.
The tax advisers suggested that Mr Chick's loan be "advanced by an entirely unconnected lender".
This was to make the transaction to look like a genuine commercial loan - however this 'unconnected lender' was part of the overall scheme - and the loan was repaid by Mr Chick's company in Mauritius.
Jim Davis - a business partner of David Chick, and an accountant - played a role in setting up the transaction.
Mr Davis is a former President of the Association of Chartered Certified Accountants in Northern Ireland.
Although Mr Davis benefitted from this loan - as it went into the Northern Ireland property company he had a stake in with Chick - we do not have evidence that Davis avoided tax by this transaction.
His role was in assisting Mr Chick in flushing money out of his Mauritian company tax free.
The Paradise Papers are a huge batch of leaked documents mostly from offshore law firm Appleby, along with corporate registries in 19 tax jurisdictions, which reveal the financial dealings of politicians, celebrities, corporate giants and business leaders.
The Nolan Show team worked alongside colleagues in BBC Panorama, the Guardian and nearly 100 media organisations worldwide.
David Chick and Jim Davis refused to be interviewed by the BBC on these matters.
In a statement their lawyers said: "Every individual is entitled to order his or her tax affairs in a tax efficient manner."
They said that the BBC's allegations were not accepted and that their clients had "paid appropriate tax on all monies earned in the UK".
With regard to that £600,000 loan, they said that Mr Chick followed "specialist advice which he would not have done if he had been given any indication that this particular transaction was not entirely legitimate".
David Chick and Jim Davis were previously shareholders in Mayville Limited alongside County Antrim brothers George and Russell Simpson.
In 2009, their company received a £1.3m grant to redevelop the old Murray's tobacco factory site in south Belfast.
Both Mr Chick and Mr Davis work from an office in the redeveloped building. When Stephen Nolan tracked Mr Chick down at the premises he asked him if he felt the taxpayers who part-funded the building were entitled to have money paid back. Mr Chick did not respond to this point.
The former chair of the public accounts committee at Westminster Margaret Hodge said she was familiar with these types of arrangements.
"I have to tell you it's an all too familiar structure which I've come to understand over time - so you set up an artificial financial structure with an artificial loan which hides the source of your money.
"It's a terrible way of arranging your financial arrangements - totally artificial - has absolutely no purpose other than to avoid tax."
In the leaked documents, Mr Chick and Mr Davis' CV boasted that they had "strong connections to Government at the highest level" and "influence at the highest political level".
When asked what they meant by this, their lawyers said their clients had no intention of responding - saying it had no relevance to the subject of the investigation.
The Nolan Show will be focusing on stories from the Paradise Papers across the week.
Paradise Papers: Full coverage ; follow reaction on Twitter using #ParadisePapers; in the BBC News app, follow the tag "Paradise Papers"