The NhRP purports to be "the only organisation working toward actual legal rights for members of species other than our own".
Its mission, according to its website, is "to change the common law status of at least some non-human animals from mere 'things,' which lack the capacity to possess any legal right, to 'persons'."
Tommy's lawsuit has already been lost in lower courts, but Mr Wise is appealing the case, based on a legal mechanism that was historically used on behalf of slaves.
"As a matter of both liberty and equality," Mr Wise has said, "Tommy should be seen as a person."
In a 65-page legal brief, the NhRP cites several specialists, such as the British primate expert Jane Goodall, to argue that chimps are "autonomous, self-determined, self-aware, highly intelligent, and emotionally complex beings who suffer from imprisonment".
As such, the animals fit the legal profile of a "person".
"Person is not a synonym for 'human being'," the brief explains, "but designates an entity with the capacity for legal rights."
Should Tommy win his case, it could lead to broader rights not only for chimps and their fellow primates, but also for other intelligent animals such as elephants, orcas and dolphins.
Mr Wise told Reuters: "The next argument could be that Tommy ... has the right to bodily integrity, so he couldn't be used in biomedical research.
"Tommy's owner, Patrick Lavery, has declined to present his case to the appeals court in Albany, but has said previously that the chimp had been on a waiting list for a primate sanctuary for three years, and that his current home was in fact a state-of-the-art US$150,000 ($190,000) enclosure.
Last year, Mr Lavery told the Albany Times Union that Tommy has "got a lot of enrichment. He's got colour TV, cable and a stereo ... He likes being by himself."
In December, Mr Wise will present a similar case to an appeals court in Rochester on behalf of Kiko, a chimp who lives in less-than-salubrious conditions in Niagara Falls.
The NhRP is expecting a decision from the appeals court in a few weeks' time.
- Independent