Her father, Fidel Castro's Argentine revolutionary companero, Ernesto "Che" Guevara, was killed in the Bolivian jungle later that same year.
Hilda Guevara, 39, the eldest daughter, whom he called Hildita (Little Hilda), died in a hospital in the Cuban capital on Monday from cancer.
Like most Cubans, Ms Guevara was troubled by the collapse of the Socialist bloc and had to confront the Communist beliefs that her father had fought and died for.
But like many of her compatriots, perhaps even most of them, she refused to turn against the man she used to call "Uncle," the man who sailed from Mexico to Cuba with her father and 80 other ragged fighters in a fishing boat soon after she was born in Mexico City in 1956.
Three years later, they overthrew the dictator Fulgencio Batista. The boat they used was called the Granma, named by its previous owner after his grandmother. "Granma" has since given her name to a Cuban province and to the Communist Party newspaper.
Although Ms Guevara was critical of some of the revolution's directions, she apparently died believing, as she told an American reporter, that "the Cuban revolution can be saved, but I have to confess I don't know how. To me, the dream is not dead. It's dormant, frozen in time. Communism has failed to keep up with the times. What I would like is a Communist system with a human face."
Her son Canek, 21, Che's grandson, a rock guitarist complete with earrings and shoulder-length hair, and a group called Metalizer, did not agree.
Interviewed by Andres Oppenheimer, an American journalist, for the book Castro's Final Hour, he did not mince his words: "This revolution is in ruins. [Che] would be proud of me. Che Guevara was a rebel. He never would have approved of what has become of this revolution."
Ms Guevara was the only child of Che's first marriage, in Mexico, to Hilda Gadea, a Peruvian. He brought them to Cuba after the revolution, where he served as a cabinet minister and married again, having four more children, before heading off to South America to spread his revolutionary dream.
His eldest daughter died as she lived, quietly, as a librarian in a government arts and propaganda centre. Few Cubans were even aware that she existed.
Wishing to interview her, I traced her recently to the big naval hospital outside Havana where even the security guards were unaware of she was.
"La hija de Che, aqu?" (Che's daughter, here?) they asked me.
I had no idea what she was being treated for but she personally came on the phone when I called her ward and then came down to the lobby in a robe, walking slowly on her husband's arm.
She looked pale and told me she did not feel up to an interview but would do so when she was released. Perhaps it was her father's aura that dissuaded my photographer and me from sneaking a photograph there and then.
By the time that Cubans learned of her death, Ms Guevara had been buried in Havana's Colon cemetery. A few dignitaries were present but there was no sign of "Uncle Fidel."
Cuban schoolchildren still begin their school day by chanting "Pioneers of communism, we shall be like Che!" Their textbooks include a letter from Che in the Bolivian jungle to Hilda for her 10th birthday on 15 February, 1966.
"Hildita dearest ... you must know that I'm still far away, and that I'll be spending a long time away from you, doing what I can to fight against our enemies. I'm not doing a great deal, but I'm doing something, and I think that one day you will be able to be always proud of your father, just as I'm proud of you.
"Remember that many years of struggle are still ahead, and when you become a woman you'll have to do your share of the fighting ... always be prepared to support just causes.
"You must struggle to be among the best in school ... in academics and in revolutionary attitude. That means good conduct, love for the revolution, camaraderie. I wasn't like that when I was your age but I lived in a different society where man was man's enemy. You have the privilege of living in a different era and you must be worthy of it."Reuse content