The 1995 execution of Nigerian playwright Ken Saro-Wiwa and eight other human rights activists (including Kiobel's husband) campaigning against environmental degradation of their native Ogoni land caused worldwide condemnation.
Saro-Wiwa came into conflict with the ruling junta when he campaigned for the Ogoni people living in Nigeria's oil basin in the South.
The popular playwright criticized Sani Abacha's military government and the powerful oil industry, charging that it had polluted and destroyed the region's land and wildlife.
The men would later come to be known as the Ogoni 9 following their executions.
Saro-Wiwa and the eight others put to death were charged with murdering four men. They were convicted and sentenced to death at a special tribunal. Throughout, Saro-Wiwa maintained that he was being framed for criticizing Abacha's regime.
Abacha ignored pleas for clemency for the men from world leaders including then US President Bill Clinton.
Nigeria was promptly kicked out of the Commonwealth of nations -- an organization made up of 52 countries that were part of the British Empire -- following the executions.
In 2009, Shell paid out $15.5 million to settle a lawsuit brought by the now late son of the deceased Ken Saro-Wiwa Jr. and others including the deceased's brother.
The suit had accused the global oil conglomerate of complicity in the imprisonment, rights violation and ultimately, death of Ken Saro-Wiwa and the eight others.
The case took 13 years to reach settlement and Shell denied wrongdoing but said it was making the payment on humanitarian grounds according to a statement published in the New York Times.
Kiobel was not a plaintiff in that suit. She and three other widows have been assisted in their long-running struggle by human rights group, Amnesty International -- a first for the organization.
"It is one of our more remarkable cases. It is very difficult to find lawyers and courts willing to take these cases," says Audrey Gaughran, acting Senior Director of Research, Amnesty International, in a phone interview with CNN.
Gaughran remains hopeful that with the evidence gathered over the years and the location of the case, the judgment will be in the claimants' favor.
"We think Mrs. Kiobel has a strong case... we believe that Shell is complicit in the execution of her husband, Ken Saro-Wiwa and the other men who were executed in 1995. We are optimistic that the court will ultimately see the same argument."
Shell Petroleum Development Company (SPDC) of Nigeria Limited, through its spokesperson, Precious Okolobo said in an email to CNN:
"SPDC did not collude with the authorities to suppress community unrest and in no way encouraged or advocated any act of violence in Nigeria.
"The executions of Ken Saro-Wiwa and his fellow Ogonis in 1995 were tragic events that were carried out by the military government in power at the time.
"We were shocked and saddened when we heard the news of the executions. SPDC appealed to the Nigerian government to grant clemency. To our deep regret, that appeal, and the appeals made by many others within and outside Nigeria, went unheard."
Kiobel's lawyer, Channa Samkalden is circumspect about a positive outcome.
"It will be a difficult case, but it is also a very important one. The evidence shows how deeply involved Shell was in the activities leading to the death of the 'Ogoni 9.'
"The fact that a court will assess that evidence and hold Shell to account will already bring some satisfaction," she said in an email interview.