In the year 2029, aboard the United States Air Force space station Oberon, Leo Davidson works closely with primates who are trained for space missions. His favorite simian co-worker is a chimpanzee named Pericles. With a fatal electromagnetic storm approaching the station, a small space pod piloted by Pericles is used to probe the storm. Pericles' pod heads into the storm and disappears. Against his commanding officer's orders, Leo takes a second pod and goes in pursuit of Pericles. Entering the storm, Leo loses contact with the Oberon and crashes on a planet in the year 3002. He discovers that the world is ruled by humanoid apes who can speak human language and treat human beings as slaves.
Leo comes across a female chimpanzee named Ari, who protests the awful treatment humans receive. Ari decides to buy Leo and a female slave named Daena to have them work as servants in the house of her father, Senator Sandar. Leo escapes his cage and frees other humans. Ari sees them, but Leo manages to convince Ari to join their cause. Leo forms a human rebellion against the apes and develops a love triangle with Ari and Daena. General Thade and Colonel Attar march ape warriors in pursuit of the humans. Leo discovers Calima (the temple of "Semos"), a forbidden but holy site for the apes.
Calima turns out to be the remains of the Oberon, his former space station, which has crashed on the planet's surface and looks ancient (the name Calima coming from the sign "CAution LIve aniMAls", the relevant letters being the only ones not covered in dust). According to the computer logs, the station has been there for thousands of years. Leo deduces that when he entered the vortex he was pushed forward in time, while the Oberon, searching after him, was not, crashing on the planet long before he did.
The Oberon's log reveals that the apes on board, led by Semos, organized a mutiny and took control of the vessel after it crashed. The human and ape survivors of the struggle left the ship and their descendants are the people Leo has encountered since landing. A battle ensues between the humans and the apes. A familiar vehicle descends from the sky and is identified immediately by Leo. It is the pod piloted by Pericles, the chimp astronaut. Pericles was pushed forward in time as Leo was, and had just now found his way to the planet. When Pericles lands, the apes interpret his landing as the return arrival of Semos, the first ape, who is their god. They bow, and hostilities between humans and apes disappear.