Giants in the Earth opens with the narrator describing the prairie setting. The novel takes place in the unsettled Dakota Territory in the 1870s. Per Hansa, his wife Beret, their two sons Ole and Store-Hans, and their daughter Anna Marie (usually called And-Ongen), have traveled for three weeks across the Great Plains, from their home in Fillmore County, Minnesota, to their destination in the Dakota Territory. The Hansas originally undertook the journey in a caravan with several other Norwegian immigrant families. One of Per's wagons broke down, however, and he insisted that the other families continue ahead of him while he repaired his wagon. Per thought that he would be able to catch up to the others in a couple of days.

The truth of the matter is that now the Hansas are lost. Per is no longer sure that they are on the right trail. In fact, there are no roads or trails, or even any signs of civilization on the prairie at all. The prairie is just an endless stretch of grassland, completely devoid of any signs of human life. The narrator refers to the prairie as a sea of grass, and he compares the wagons to ships. The Hansas' meager earthly possessions include two small, dilapidated wagons that are hitched together and move at a snail's pace; the oxen that are used to pull the loaded-down wagons; and a cow named Rosie that provides them with milk.

Per and his eldest son, Ole, walk ahead of the two wagons. Per tries desperately to scan the horizon to find the other wagons. Although he has doubts about whether he will find the other families, he remains optimistic at heart, reassuring both Ole and Beret that they will soon find the others. Meanwhile, Beret drives the oxen and takes care of Anna-Marie between fits of silent weeping. Beret is afraid of the new land and she does not like settling in such an uninhabited area.

As the sun sets, Per decides to stop for the night. Each member of the family performs his or her own chores to ready the campsite: Ole and Hans fetch wood and prepare a fire, Per milks Rosie and makes beds for everyone under the wagons, and Beret makes the meal of porridge and milk. When dinner is over, the family prepares for bed. After making sure that the children are asleep, Beret asks Per if they will ever find the other families again. Per tells her that he is certain that they will.

Plagued by self-doubt, Per is unable to sleep during the night. He senses Beret silently reproaching him for getting them lost and for making her leave her home in Norway. He knows that she did not want to immigrate to America and that she would have much preferred to stay in her home country. Per makes sure that everyone else is asleep, and then he gets up and dresses quietly. He explores the land around his campsite to decide which direction they should take the next day.

Per walks for several miles until he stops at a wooded thicket. He comes upon a clearing where he finds a recently abandoned campsite and some fresh horse dung. Nearby, he notices a creek and sees a dried mutton leg at the edge of the creek. He is overjoyed because he knows that this mutton belonged to his friend Hans Olsa, who was also making the journey West. Per now knows that he has found the right trail. He returns to his camp, where he is surprised to find Beret awake, waiting for his return. She cries and tells him that she is afraid, but he comforts her by telling her that he has found the trail.