Superquinn says it will accept Irish notes and coins in all 19 of its shops for three days next week.
The supermarket says it will accept the old money in payment or part payment for goods to allow their customers "get rid of their old currency once and for all".
The Central Bank of Ireland estimates £358 million worth of Irish notes and coins have still not been exchanged.
With retail banks no longer taking the money, the only place to exchange it is in the Central Bank in Dublin.
Superquinn believes the scheme, which runs February 17th to 19th, will be particularly attractive to people living outside Dublin.
Deputy chairman Mr Eamonn Quinn said practically every day a number of customers ask if they can use Irish money to pay for their shopping.
"It's clear that most people still have small amounts of money lying around and have not found it convenient to exchange it or have forgotten to do so," he said.