The appeals court in New York state said caged chimpanzee Tommy could not be recognised as a “legal person” as it “cannot bear any legal duties”.
The Nonhuman Rights Project had argued that chimps who had such similar characteristics to the humans deserved basic rights, including freedom.
The rights group said it would appeal.
In its ruling, the judges wrote: “So far as legal theory is concerned, a person is any being whom the law regards as capable of rights and duties.
“Needless to say, unlike human beings, chimpanzees cannot bear any legal duties, submit to societal responsibilities or be held legally accountable for their actions.”
The court added that there was no precedent for treating animals as persons and no legal basis.
In October, the Nonhuman Rights Project had argued that chimpanzees should be recognised as “legal persons” and therefore be given the right to liberty.
The group said on Thursday it would appeal against the court verdict in New York’s highest court.
Tommy’s owner, Patrick Lavery, said he was pleased with the outcome, according to the Associated Press.
Tommy – who is believed to be about 40 years old – is a former entertainment chimp. He was given to Mr Lavery about 10 years ago.