The main character is Ham III the grand son of Ham the chimp who was first in space. Number three lives in the shadow of his revered ancestor and finds his work in a circus demeaning but it does not challenge him and he is safe there where he can't be compared to his ancestor.
Through a twist of fate he finds himself on a trip across the Universe through a worm-hole to visit a newly discovered planet. Also on the trip are Titan the macho monkey and Luna the smart girl who Ham has eyes for.
With a little bit of "you can do anything you want" as part of the script Ham, as we would suspect, becomes a hero on the mission which is undertaken by the chimps because it may be too dangerous for humans. All of this is forged by a Senator who stops and continues the space program at will as if he were President.
Little Kilowatt, a little bright bulb character from the new planet, helps the heroes travel through dangerous terrain to save Titan who has been captured by an insane dictator who is willing to kill most of the population of the planet when the three suns line up and a volcanic explosion occurs.
With modest animation and a lot of yelling by Ham the predictable story moves back and forth through the worm-hole until Ham is a hero and believes he has done his grandfather proud. His grandfather however would not have been happy with this minimally entertaining film.