In the future, Keith wins a Presidential election against Deutscher. A rich man, Eckles, listens to the results as he takes an elevator to Time Safari, Inc. An agent greets him while discussing the election results, noting that Deutscher would have been a dictator. Eckles presents his ID and tries to pay, but the agent says he pays upon return. He then shows Eckles photos of dinosaurs, and assures him they were taken yesterday… 60 million years ago. Eckles examines the photos of Tyrannosaurus Rex and is eager to be off.
The agent takes him to meet with the hunting party, lead by safari guide Travis. The agent tells Eckles that if he fails to obey, there's a penalty of $10,000 plus government action. Travis reviews Eckles' biographical information and confirms that he's a big game hunter, and hunts illegal animals. Eckles insists that he shot them to protect himself, but admits that he's bored so he came to Time Safari. Travis tells him to choose a weapon and assures him that they are all capable of killing a dinosaur. He then has Eckles sign a waiver, warning that they've lost six safari guides in the past. Eckles is offended but has no choice.
Once he's suited up, Eckles accompanies Travis and the other two hunters to the time sphere. They enter and Travis sets the controls for 60 million years in the past. Eckles stares out in awe and admits that any hunter would envy them, and insists that he's ready.
The sphere arrives in the past and Travis extends a metallic path a few inches above the ground. He warns the hunters that they are not to step off the path under any circumstances. They are only allowed to shoot one dinosaur. Travis warns that the government doesn't like time traveling and the pay big fees to get permission. They could potentially destroy an important link in a species. Eckles is unimpressed.
The party leaves the sphere as Travis explains that if they kill a mouse, they kill all of its million descendents. The repercussions are potentially endless, and could wipe out whole races of people. Eckles jokingly agrees, chuckling. The hunters proceed along the path and Travis explains that their target is marked with white paint. He scouted the area earlier and located a Tyrannosaurus Rex fated to die from a falling tree three minutes after they shoot it.
They approach the marker on the path and the dinosaur arrives. It chews on an old kill and Travis tells the hunters to prepare. It advances on them and Travis tells them to time the shot to the second before the tree falls. Eckles panics and Travis tells him to go back to the machine. The big game hunter admits that he can't move and the other two hunters prepare to shoot at the designated target. Eckles stumbles off the path and Travis sees him, and then tells the other hunters to open fire. As they fire, Eckles shoots wildly into the trees and the dinosaur, and Travis fires the killing shot. The tree falls onto the dying T. Rex a second later.
Travis turns to Eckles and tells him to get back onto the path. Eckles stumbles over and Travis hands over his knife. He tells Eckles to dig out the bullets so they don't leave anything in the past that might disrupt history. Eckles reluctantly does so while Travis uses a magnet to get the other shots out of the foliage. Nauseated, Eckles tries to complete his task while other dinosaurs move in. Travis taunts the big game hunter, asking if he'd like to stay behind to greet them. Once Eckles gets the bullets, Travis tells him to get out of there.
Travis pilots the time sphere back to the present. As they return to the equipping chamber, a man wearing a military uniform greets them. Travis goes into the main office and discovers that the Time Safari's sign is now in a slightly different language. All of the staff wears military uniforms and there are armed guards everywhere. Travis asks who won the election, and the agent says there was no election and Deutscher is the leader of the 15th Rule. Travis stares at Eckles, shoves him onto a chair, and examines his boot. Stuck on the bottom is a dead butterfly. Furious, Travis draws a pistol and shoots Eckles.