But that has angered workers at the distribution centre, who say Foodstuffs - which owns Pak'nSave - is trying to bully them into silence over problems with their employment.
First Union, which represents the workers, says in fact the chicken shortage is due to the company contracting out the chicken distribution to another company, East Tamaki-based Icepak NZ.
Documents seen by the Herald confirm Foodstuffs is leasing space at Icepak.
Union spokeswoman Lisa Fox believes it's a standover tactic to make the workers believe their jobs will be outsourced if they don't back down.
She described Pak'nSave's attempt to blame workers taking strike action for their own failure as a "cynical tactic by a nasty company."
"We're in a dispute with Foodstuffs, the co-operative run by Pak'nSave and New World owners, over their repeated refusal to recognise long-serving labour hire staff as employees.
"Now Foodstuffs has outsourced its chicken distribution to a new company, probably as an attempt to make current staff worry about their job security," said Fox.
"But now the new contractor can't fulfil orders and the company is blaming their own staff."
A notice apparently written by supermarket management said there was no chicken "due to industrial action". Photo/Supplied
The workers are technically employed by temping agency Drake International, which provides workers to the CTD Nesdale cold store centre in Wiri.
First Union argues the workers are on zero-hour contracts, are discouraged from taking sick leave and can be laid off at any time with no notice. Despite some working in dangerous, often below-freezing conditions for up to 60 hours a week, most earn barely above minimum wage.
Last month workers at the site staged two 'walk-offs' in protest, but Fox said after they returned to work the chicken delivery operation returned to normal.
The Foodstuffs-owned distribution centre of frozen food, CTD Nesdale, has confirmed the sign was not correct.
"The sign an employee put in a store chiller was not correct, as the disruption relates to the change in supply, not union negotiations," CTD Nesdale Chris Quin confirmed.
He explained to Newshub that the shortage of chilled and frozen products was the result of a recent supply change.
"The claim that this is somehow a threat to staff is incorrect," he said, adding that the sign had been removed.
The Union demands an apology to the workers.
"We want the company to apologise to its workforce for the misleading statement and tell their customers the truth," said Fox.
