Sometime in the future, Presidential candidate Keith wins the election against his rival, Deutscher. Rich big game hunter Eckles isn't interested: he's on his way to Time Safari, Inc. The clerk finishes his discussion with a coworker about how Deutscher would have been a dictator, and then turns to Eckles. The hunter gives his ID and offers payment, but the clerk informs him that he pays up on his return. He then shows Eckles photos of dinosaurs and explains that they were taken one day prior... and 60 million years ago at the same time. Eckles is impressed by the photo of a Tyrannosaurus Rex and is ready to leave.
Next, Eckles meets with the safari guide, Travis. The clerk warns Eckles that there is a $10,000 fine if Eckles fails to obey Travis' instructions, and the government may take further action. Travis checks Eckles' ID and notes that he illegally hunts wild animals for sport. Eckles claims that he shot them in self defense, and then says that he's grown bored at the lack of challenge. He wants to hunt the ultimate animal and hopes Time Safari can make it happen. Travis has him choose a weapon and then asks him to sign a waiver. When Eckles balks, thinking that his courage is being challenged. Travis warns that they've lost six safari guides during past expeditions and it's mandatory. Eckles reluctantly signs.
Once he selects his weapon, Eckles follows Travis and the other two hunters into the time sphere. As they depart, Eckles talks of how they are going on the ultimate expedition and would are the envy of hunters everywhere.
They arrive in the past and Travis extends an anti-gravity path out into the jungle. He explains that the hunters must stay on the path no matter what and are only allowed to shoot the designated dinosaur. Stepping off the path could disrupt a link in a species' evolution, but Eckles isn't interested. As they leave, Travis explains that killing a single mouse could have a chain reaction that could cascade through the millennia, wiping out generations of mice and ultimately causing cavemen to starve and Europe to fall into desolation. Eckles doesn't take the warning seriously. As they proceed along the path, Travis explains that earlier, he traveled back to a few minutes before their arrival, located a Tyrannosaurus Rex that will die at the designated time due to falling paint, and marked it with white paint.
The hunting party stops at the marker on the path and the Tyrannosaurus Rex approaches them. Travis tells them that they must shoot at the precise second before the tree falls, and they must wait for his signal. As the enormous dinosaur approaches them, Eckles panics and Travis orders him back to the time sphere. Eckles freezes momentarily and then stumbles back off the path. With the dinosaur closing in fast, Travis orders the other hunters to shoot. Eckles opens fire in a wild burst of gunfire, spraying bullets everywhere. Travis finally fires the killing shot, and the tree falls on the dinosaur a second later.
A disgusted Travis orders Eckles to get back on the path and then dig the bullets out of the dinosaur with a knife. As he uses a magnet to retrieve the other bullets, a nauseated Eckles recovers his bullets. As other dinosaurs approach, Travis disgustedly suggests that he might leave Eckles in the past, but finally tells him to get back to the time sphere.
The hunting party returns to the present and discover that the man in charge of their equipment is now wearing a military uniform and speaks with a European accent. They step into the main room and discover that the greeting sign has subtly changed. All of the staff wear uniforms and carry firearms. Travis approaches the clerk and asks who won the election. The man responds by saying there was no election and that Deutscher is the glorious leader of the 15th Rule. Realizing that something has gone horribly wrong, Travis shoves Eckles into a chair, reaches down, and plucks a dead butterfly stuck in the mud on the hunter's boot. The guide lets the butterfly drop to the ground and then pulls his pistol and shoots Eckles for condemning them all.