The death has taken place of Dolours Price, who was jailed for her part in the IRA bombing of the Old Bailey in March 1973.
The 61-year-old was originally from Belfast, but had been living in Malahide in Dublin.
A post mortem on the circumstances of her death will be carried out, but gardaí say at this stage there is no indication that foul play was involved.
Ms Price was a centre of controversy in recent months after she gave a number of press interviews in which she claimed she drove Belfast mother-of-ten Jean McConville to the place where she was murdered by the IRA.
She also alleged that Sinn Féin President Gerry Adams personally ordered the abduction of several people the IRA considered to be traitors in the 1970s.
Mr Adams has always denied ever being a member of the IRA.
Ms Price was part of an IRA team that blew up a number of buildings in London, including the Old Bailey, 40 years ago next March.
Her sister, Marian, was part of that group.
Gerry Kelly, now a prominent Sinn Féin member at Stormont and a representative on Northern Ireland's Policing Board, was also a member of the group. He was 19 at the time.
All were arrested attempting to board a plane at Heathrow and were given lengthy prison terms after a trial.
During a campaign to be transferred to prison in Northern Ireland, the Price sisters went on hunger strike and were force fed.
Eventually they were repatriated and in 1981 they were released from Armagh prison on humanitarian grounds.
Marian Price is currently in prison in Northern Ireland after she was arrested following a dissident republican event in Derry in 2011.
Mr Adams has offered his condolences to the Price family.
"I want to express my profound sadness at the news of the death of Dolours Price," he said.
"I want to extend my sincere condolences to her family and especially to her two sons, Danny and Oscar, and her sister Marian.
"Marian should be released from detention," he added.