When he travels into the pre-historic past, Eckels steps off the anti-gravity path made by Time Safari, Inc., and in so doing, he kills a butterfly. This act has consequences that reach all the way to present time.
At the beginning of the story, it is a nervous Eckels who arrives at the Time Safari, Inc., office:
A warm phlegm gathered in Eckels’s throat; he swallowed and pushed it down.
The man at the desk introduces Eckels to his guide, who is named Travis, and he gives Eckels instructions on what the trip is like and how he should conduct himself. When Eckels, his guide and the others arrive, Mr. Travis instructs Eckels very precisely on how to shoot the dinosaur that he has paid to hunt. Then Travis points to the Path that has been laid by Time Safari. This anti-gravity metal floats above the ground so that the men can walk without touching so much as a blade of grass. In this way nothing from the Past will be changed.
"Stay on the Path. Don’t go off it. I repeat. Don’t go off. For any reason! If you fall off, there’s a penalty. And don’t shoot any animal we don’t okay."
Eckels is also told that he absolutely must not step off this path because if he does, he can change the entire history of the world. This warning proves to be true. When the massive Tyrannosaurus Rex thunders out of the jungle, Eckels becomes paralyzed with fear, and tells his guides that he miscalculated on the dinosaur's size. "This is too much for me to get hold of." An angry Travis instructs Eckels to get back on the time ship and hide there. But, because he is so frightened, Eckels steps off the path.
Upon his return to Safari Inc., Eckels surprisingly finds things greatly altered. President Keith's opponent has won the election; the words on signs are illegible to Eckels. There is a slight chemical smell in the air, and the man behind the desk is not the same one as when he first arrived. Nervously, Eckels recalls what he was told about the path, and he fumbles with the slime that is on his boots.
Embedded in the mud, glistening green and gold and black, was a butterfly, very beautiful and very dead. “Not a little thing like that! Not a butterfly!” cried Eckels.
He cannot imagine that the death of this insect has so altered his world. Eckels drops to his knees, begging to take the insect back, to return everything to the way it was. But it is too late. For, he hears Travis click the safety catch of his rifle, and "there was a sound of thunder."