A NASA space probe is sent through a wormhole and crash-lands on a distant planet ruled by the tyrannical alien dictator Zartog. To recover the probe, NASA recruits a team of chimps for an intergalactic mission. Among the team are Ham III, a laid-back circus chimp and grandson of the famous Ham, the first chimpanzee in space; Luna, a fearless and intelligent pilot; and Titan, the team’s brave and loyal leader. Ham III initially sees the mission as a fun adventure, not taking it seriously, while Luna and Titan focus on the gravity of their task. They embark on their journey and face various cosmic challenges on their way to the alien planet.

As the chimps arrive on the planet, they discover its inhabitants living under the oppressive rule of Zartog, who uses the technology from the crashed probe to dominate them. The chimps must rely on their individual strengths and newfound teamwork to navigate dangerous terrain and evade Zartog's minions. With the freedom of the planet's residents and the probe’s retrieval at stake, the chimps' mission intensifies, forcing Ham III to grow into his heritage and take on real responsibility. The team's bond strengthens as they face the ultimate challenges in their quest to defeat Zartog and complete their mission.