Austrian animal rights group VGT brought the test case before the court on behalf of a British woman, Paula Stibbe. She has applied to become the legal guardian of a chimp named Hiasl, who would otherwise face detention in a laboratory.
Jan Creamer, chief executive of ADI, said: "This case is very timely. It is time for humans to re-evaluate our relationship with our closest relatives. Primates fulfil all the necessary conditions for personhood."
If VGT succeeds, Hiasl, taken to Vienna from Sierra Leone in 1982, will be granted rights against detention and torture. He will not, however, be given any rights that confer responsibility.
Hiasl would also be entitled to keep any money donated to his cause, and some activists believe his guardian could then consider legal action against the vivisection laboratory on his behalf.