In the seven days since the enrolment process began, 588 residents of the town have agreed to take part in the project which would see participating adults receive a monthly universal basic income (UBI) of 2,500 francs ($2,570) for a year.
This means the woman behind the experiment, Swiss filmmaker Rebecca Panian, has almost hit her target of at least 650 participants.
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This figure equates to half the population of Rheinau and she considers it the absolute minimum level of participation required before the fundraising stage of the project can go ahead.
The money for the 12-month UBI project would come from crowdfunding or donations from institutions, with the total cost of the experiment estimated at three to five million francs.
If Panian can secure funding, she plans to film the results accompanied by a team of four researchers including sociologists, an economist and a media linguist.
Panian was inspired by the 2016 referendum in which Swiss voters overwhelmingly said no to the idea of a UBI of 2,500 francs over concerns about how it would be funded as well as fears it could jeopardise the country's existing social welfare system.
But Panian strongly believes the idea is worthy of an in-depth practical experiment and not just discussion.
The deadline for enrolment in the project is September 17th but only residents who moved to Rheinau before June 5th are eligible to take part.
In another catch, participants who earn more than 2,500 francs, even if that money comes from social welfare, will be required to repay any money received during the 12-month period if the experiment goes ahead.