It is the first confirmation from a republican source that Chesney was an IRA activist. Last week, the police ombudsman's report named the priest as a suspect in the atrocity.
RUC special branch alleged he was the Provisionals' South Derry commander and drove the lead bomb car into Claudy. However, given special branch's history, many nationalists are suspicious of its claims.
The former senior IRA figure said Chesney was definitely an IRA member: "Like many others, he joined following that wave of anger at how civil rights' marchers were treated. He was deeply affected by the introduction of internment."
The ex-IRA man attended a meeting in Bellaghy, Co Derry, at which Chesney was present. He was "very impressed" with Chesney: "He wasn't just a verbal republican. He wasn't afraid to get his hands dirty."
The ex-Provisional was in jail at the time so he doesn't know if Chesney played a role in the bombing.
In 1973, the Catholic Church moved the priest to Malin Head, Co Donegal. The former IRA man claimed Chesney was instrumental in setting up a training camp in the area which was used right up until the 1994 ceasefire.
Former IRA chief of staff Ruairí Ó Brádaigh said the priest had denied involvement in Claudy to him.
"Fr Chesney approached me in 1979 in Sligo after I'd addressed a H-Block rally. He said there were rumours that he was involved in Claudy but he had nothing to do with it and was on holiday in Donegal at the time of the bombing."
Meanwhile, Deputy First Minister Martin McGuinness, who was the IRA's Derry OC at the time of the bomb, has been urged to be honest with bereaved families.
"The names of the senior republicans involved... are common knowledge. These individuals must do the decent thing and tell the families the full truth," said SDLP councillor Brenda Stevenson.
"As a party in government, Sinn Fein must live up to its responsibilities. Letting it all hang on Fr Chesney who is dead is the cowardly way out."
SIC: ST