Olive is mailed the small, mysterious African animal Eugene the Jeep by her uncle Ben Zene Oyl, which eventually emerges from the crate before the eager eyes of Olive, Popeye, and Olive's parents Cole and Nana.
The ambitious Mr. Chizzelflint knows about the Jeep's "four-dimensional brain" - which can answer every question about the past, present and future - and plots to get Popeye out of the way so that Olive will sell him the animal. This involves hiring hitmen to eliminate the sailor. All these plans fail, including an attempt to get Wimpy to assassinate Popeye, as the moocher is not as easily persuaded.
Wimpy also learns of Eugene's divination powers, then proceeds to ask the Jeep about racing horses. Wimpy understands the animal's affirmative signs (bending down and pointing the tail upwards) and is able to win money on the track, rewarding his little friend with orchids (the only thing a Jeep will eat). Even as Mr. Chizzelflint offers a million dollars for the creature, Olive, with Popeye's help, realizes this makes Eugene too important and again declines. For not even Chizzelflint is fully aware of the extent of the Jeep's powers, exemplified by his ability to pass through walls. Olive is also quite fascinated by the Jeep and follows Wimpy to throw her own money into the horse races. Popeye is "disgustipated" by their actions.
Later, Popeye signs up for a prize fight against revered heavyweight champ James J. Jab. Popeye is confident about this fight, until he learns that, apparently, the Jeep has predicted that Popeye will lose against James. Popeye is absolutely devastated by it, especially since he has not lost in a fight before and thinks that this defeat will make him an embarrassment in front of all the admiring children. Somehow, James Jab's agent also hears of this, and decides to bet $1,000 on James. Things go even further south as Olive and Wimpy also decide to bet on the sailor's opponent, and even refuse to express any good will towards Popeye in fear of altering the future.
Popeye's anxiety hurts him so much ("BUT THE JEEP!! The Jeep said he'd lick me... ") that he quickly falls ill and is promptly sent to the hospital. The doctors cannot fully inspect his physical state or operate on him due to his tough skin, and decide that he needs to stay in bed for a few months.
When the fight against James Jab comes, an ambulance carries Popeye to the ring. Wimpy is the referee, as usual. Despite his physical state, Popeye still puts up quite a fight, being thrown around the ring without actually being hurt, and knocking down James with ease multiple times. However, Wimpy refuses to count down as he is still convinced the Popeye will lose. On the other hand, Olive has a change of heart as she still desperately wants Popeye to win. Eventually, Wimpy relunctantly sends off James, who gets carried away on a stretcher, while Popeye wins the fight. Olive is mad that Eugene has lied to them, but they later find out that the Jeep can be distracted by bugs, and his poses may be misinterpreted as the answer to any question.
At the end of the storyline, Popeye starts to have a feeling that his father is not dead, and hesitantly asks the Jeep about it, leading to the next storyline, "The Search for Popeye's Poppa".
- This storyline has the same premise as the earlier "Dice Island", in which another small African animal with mysterious powers (Bernice the Whiffle Hen) is given to a member of the Oyl household (Castor Oyl).
- The subplot of Wimpy winning money on the horse track with the aid of supernatural foresight was adapted for the live-action film Popeye, yet there it was Swee'Pea who had divination powers instead of Eugene (who is absent from the film).