Warning: Wikipedia contains spoilers
The story features Donald and his nephews as members of a museum sponsored expedition searching for the source of a number of square "artifacts" held in the Duckburg museum, recently revealed to be square eggs! There is a rising interest, both scientific and financial, to find the source of these eggs and the chicken that gave birth to them. The only thing known about them though is that they came from somewhere in the Andes. Unfortunately for the members of the expedition they all suffer from food poisoning during their journey to South America and by the time their boat reaches its coasts the only ones that had recovered enough to continue the expedition were the youngest in the group and the lowest in hierarchy: Donald and his nephews.
Their search for the square eggs in the Andes seems hopeless as the local population sees them either as insane or as suckers to be fooled into buying artificial eggs. Finally they manage to find a very old man who can help them. He tells them the tale of an unknown man who had brought the eggs with him. The man was found by his father and himself, as a young child exhausted. He had come out of a mountain area eternally covered in mists. Despite their efforts the man did not recover and his sleep prooved to be eternal. He remembers his father selling the eggs they hold in their hands.
The Ducks follow the dead man's path into the mists and after efforts of days they find a populated valley in the Mountains, hidden by the mists. The local inhabitants speak with an old Southern American accent taught to them by their previous visitor, the dead man, a professor from Birmingham who had discovered their valley during the late 19th century. After a stay in the valley, they manage to convince the very hospitable locals to let them go. The latter are sad to see them go cause they were a source of information from the outside world to their small and isolated civilisation, even if they had committed a sacrilege by presenting a circle.
Bringing many square chickens and eggs with them the Ducks again struggle to escape from the mists. Finally when they do manage it they are nearly exhausted and only two chickens are alive, they had to eat the rest. But it is only when they return to Duckburg that they realise the entire expedition was a failure. Both of the chickens are male and naturally can't reproduce. The story ends with Donald now giving an angry response to whoever mentions eggs and chicken to his face.Plot