The story begins as a young alien woman named Dusk arrives on Earth to warn the population that a giant extraterrestrial being, known as the Sun-Eater, is heading our way. Dusk is a member of an unknown alien race, and does not speak or understand a word of English, so Saturn Girl uses her telepathic powers to translate for her. Dusk has attempted to warn hundreds of worlds, prior to Earth, about the Sun-Eater. Each planet had tried, in its own way, to stop the Sun-Eater, but every attempt was as unsuccessful as the last one. This has convinced Dusk that the Sun-Eater is indestructible.
Despite her warnings, the Justice League still try to stop the Sun-Eater. For their first attempt, Mr. Miracle tries using his boom tube to send it into another dimension. This proves unsuccessful, since they discover that the Sun-Eater is not entirely in our dimension. As a last resort, Superman and several other "heat-producing" heroes combine their energies to create a second sun and try to lure the Sun-Eater away from Sol. The Sun-Eater quickly consumes that sun before moving on to Sol.
As Sol is extinguished, Earth falls into chaos, and the planet starts to freeze. Powerless (especially Superman, since his powers are fading due to the lack of sunlight) to do anything to stop the freeze, the League tries to help control the chaos and to keep hope alive. Many people freeze to death. Wildcat is badly injured. Etrigan the Demon offers the entire world heat at the cost of their souls; the world rejects him. Lex Luthor teams up with the League to try to reignite the Sun.
The events of this series cross over into other books as well. Superman encounters Ferro Lad, who would later make an abortive attempt to destroy the Sun-Eater. The Ray devotes his attentions to a small Mexican town. Tommy Monaghan (Hitman) holes up in his favorite bar, Noonan's.
Seeing Earth as just another failure (and after being attacked by an angry mob who had accused her of bringing the Sun-Eater to Earth), Dusk decides its time for her to move on. As she prepares for take-off, she encounters a stranger, and is shocked that he understands her language. The stranger takes Dusk on a quick trip around the world and shows her the League's efforts to keep hope alive. Dusk doubts that there's any hope left for the world. Eventually, the stranger disappears and Dusk is left alone in an alleyway. She is found by a small group of people and, thinking they are going to attack her again, prepares to defend herself. To her surprise, the group offer to take her to a shelter where she will be safe. This act of kindness gives her hope for the planet.
The assembled heroes construct a technological means of destroying the Sun-Eater. Lex Luthor angrily bows out of piloting the ship needed, revealing that he was in it simply to save his own skin. Ferro Lad steals the ship, only to be shunted back to earth by Hal Jordan, the former Green Lantern then known as Parallax. Parallax sacrifices his life to reignite the Sun.
The League watches in astonishment, and Dusk says she no longer believes anything is impossible.