The proposal, launched by an animal rights activist group called Sentience Politics in 2016, called for an amendment to the constitution in the northern half-canton of Basel City to include “fundamental rights to life for non-human primates”.
The animals are “highly complex beings, possessing an intrinsic, essential interest in living a life of bodily and mental integrity,” the group said.
“Non-human primates need to be protected by fundamental rights which guarantee that their essential interests are respected,” it said, pointing to a right to life, as well as to physical and mental integrity.
Campaigners collected the required 100,000 signatures needed to put basically any issue to a popular vote in Switzerland's famous direct democratic system.
But the cantonal and city governments opposed a vote, warning it could violate federal law.
A Basel court dismissed the first complaint against the initiative's legality last year, and on Wednesday Switzerland's top court rejected the appeal against that decision.
“In principle, cantons can go further than the protections guaranteed by the federal constitution,” the court said in a statement.
“The initiative does not ask that federal rights accorded to humans be extended to animals, but is asking for the introduction of specific rights for non-human primates,” it said.
“While unusual, this does not in itself contradict the superior law, especially since the fundamental distinction between animal rights and fundamental human rights is not brought into question.”
Following the ruling, Sentience Politics told the ATS news agency it was “thrilled at this historic decision”.
While there are no more roadblocks in the way of putting the issue to a vote, it remains unclear when voters will have their say.
In Switzerland, which stages popular votes and referenda at the national, regional and local levels every few months, it can take years from the time such initiatives gather the necessary signatures until they make it onto the ballot.