The ship, which was christened the Greenpeace, was intercepted by the U.S. navy and never reached the Alaskan island of Amchitka.
But the stunt generated a barrage of media attention for a group of activists calling themselves the Don't Make the Wave Committee, who were happy to take credit the following year when the U.S. officially banned testing on the island.
It marked the birth of an international movement that has a long and controversial history fighting against issues such as climate change, nuclear waste and whaling, often staging grand stunts that end in arrests, criticism and, most importantly, headlines.
The group, which long ago adopted the name Greenpeace, is returning to Vancouver this week to mark its 40th anniversary.
"The remarkable thing about 40 years is that the organization is still standing -- and not only is it standing, it's thriving," says Greenpeace International's executive director, Kumi Naidoo, who will be on hand for the anniversary.
Vancouver's mayor will proclaim a "Greenpeace Day" on Thursday. A so-called "Rainbow Warrior Festival" is planned this weekend at a local beach.
After its birth as an anti-nuke group, Greenpeace quickly expanded its focus and reach.
By the late 1970s, the group became Greenpeace International, with its head office now located in Amsterdam, and branches have opened in dozens of countries around the world.
Soon the group was staging dramatic high-seas confrontations to protest seal and whale hunting, the dumping of radioactive waste and driftnet fishing. Then came campaigns to protect the Antarctic, fight climate change and oppose the forestry industry, among other causes.
Naidoo says Greenpeace's tactics of grabbing headlines with elaborate stunts was borrowed from the civil disobedience of the U.S. civil rights era.
In Canada, Greenpeace has staged events to protest Alberta's oilsands and this country's record on climate change. In 2009, nearly two dozen people were arrested during a protest in Ottawa when activists draped banners on Parliament opposing the government's climate change policies.
Greenpeace is among several groups planning what's been described as a civil disobedience campaign on Parliament Hill later this month to protest TransCanada's proposed Keystone XL pipeline, which will transport oilsands crude from Alberta to refineries on the U.S. Gulf Coast.
Naidoo, a South African-born former anti-apartheid activist, stresses that Greenpeace's campaigns, while often controversial, are peaceful.
He describes Greenpeace's tactics as "non-violent direct action," which use provocative messages that stick in the memories of the public and politicians.
"Often, it's not just speaking out against injustice but also exposing that injustice," he says.
"The reality of the world we live in is you cannot try to successfully communicate to people in jargonistic language, in scientific language. So as long as we do what we do peacefully, so long as we stay true to the principles of active non-violence, then I think it is not only legitimate, but it is the right thing to do."
They are tactics that have earned Greenpeace criticism, and while the stunts may start peacefully, they haven't always ended that way.
In 1985, the group planned to protest nuclear weapons testing in the South Pacific by the French government. France's intelligence service deliberately sank the ship, and the explosion that took the ship down killed Greenpeace photographer Fernando Pereira.
Beyond its tactics, the group has also come under fire for its politics, which critics have described as too extreme and in some cases not supported by science.
One vocal critic was one of the group's early members.
Patrick Moore was on the Greenpeace ship during that first voyage in 1971, and he stayed with the group for 15 years. He now runs a consulting company in Vancouver that sees him advocate for industries such as nuclear power.
Moore says Greenpeace is too extreme and "dogmatic," taking positions that he says don't make sense if the goal is environmental sustainability.
Among the issues where Greenpeace and Moore disagree are Greenpeace's opposition to nuclear energy, large-scale hydroelectric projects, the forestry industry and aquaculture. Moore argues all of those industries can be sustainable, and accuses Greenpeace of putting politics over science.
"They focus a lot on sensationalism, they're not afraid to use misinformation, and they use fear as the main motivators to get people to support them," he says.
"People think I left Greenpeace because they became too extreme in their tactics. Not at all. It was because they became too extreme in their positions."
Moore's criticisms have earned him derision from Greenpeace, which writes him off as a paid spokesman for the nuclear industry. Greenpeace accuses Moore of using his past affiliation with the group to gain legitimacy.
Moore bristles at those accusations, which he says are little more than "name calling." And despite his falling out, Moore says he still has fond memories of his time with the group.
"It was absolutely amazing. We really had power and we really made change, and it was like being part of a really important revolution," says Moore.
"It was a gift for me to be where I was and have that opportunity."
Shi-Ling Hsu, who teaches about climate policy and environmental law at the University of British Columbia, argues Greenpeace has actually hurt the credibility of the environmental movement by taking positions that aren't fully supported by science.
Specifically, he points to Greenpeace's comments linking disasters such as hurricane Katrina, which devastated New Orleans and the surrounding area in 2005, to climate change, and the group's eagerness to label certain chemicals as carcinogenic.
"What they do best is press buttons, rather than giving a voter or a consumer a real feel for the problem. I think they think if you scare people, that's how you get them to pay attention," he says.
"It dilutes the quality of my message and other people that are trying to say that we should pay attention to these environmental problems."
For all its critics, Greenpeace has a long list of defenders, too.
Among them is Vancouver's mayor, Gregor Robertson.
"Greenpeace has a storied history globally of making a huge difference on both peace and environmental issues," says Robertson.
"The controversy on the given day with their tactics or their issues fades over time. And if you look back 40 years, the issues they've championed are very well accepted now and positions that society has embraced. They've tended to be ahead of their time."
Greenpeace's executive director says the group's work -- including its trademark tactics -- must continue. Naidoo says many of the problems they've targeted persist -- and in many cases have only grown worse.
"Our efforts have to be intensified, because time is running out when it comes to catastrophic climate change," he says,
"The sad thing is people in the developing world who are the least responsible for climate change are the ones whoare paying the most brutal price now. It cannot be business as usual, and for us it cannot be activism as usual."