A reflective statue is found at the bottom of one of Earth's oceans, having lain there for 1.5 billion years. Since humans have recently developed a time-slowing field and found that one such field cannot function within another, it is suspected that the "Sea Statue" is actually a space traveler within one of these time fields. Larry Greenberg, a telepath, agrees to participate in an experiment: a time-slowing field is generated around both Greenberg and the statue, shutting off the stasis field and revealing Kzanol. Kzanol is a living Thrint, a member of a telepathic race that once ruled the galaxy through the Power (mind control).
Eons ago, Kzanol's spaceship had suffered a catastrophic failure; its reactive drive system failed and the navigation computer automatically jettisoned it. Faced with insufficient power to use hyperspace, Kzanol aimed his ship at the nearest uninhabited Thrint planet used to grow yeast for food (Earth), and turned his spacesuit's emergency stasis field on to survive the long journey and impact. He also arranged for his ship to change course for the system's eighth planet (Neptune) after he was in stasis, with his amplifier helmet and other valuables stashed inside his spare suit (in order to hide these valuables from any rescuers).
Although he assumed that the resident Thrint overseer would be able to rescue him after seeing the plume of gas created by his impact, his timing could not have been worse; while he was in stasis, the races enslaved by the Thrint revolted. Facing extinction, the Thrint decided to take their enemies with them by constructing a telepathic amplifier powerful enough to command all sentient species in the galaxy to commit suicide. (Only the artificially created Bandersnatchi survived, having been secretly designed to be resistant to the Power.) After hundreds of millions of years, the yeast food mutated and evolved into complex life on Earth.
The telepathic encounter with the Thrint leaves the confused Greenberg with two sets of memories, his own and Kzanol's. He instinctively assumes he is Kzanol, the much more powerful telepath. Both Greenberg and the real Kzanol steal spaceships and race to reclaim the thought-amplifying machine on Neptune, which is powerful enough to enable a single Thrint to control every thinking being in the Solar System. The chase leads to Pluto, which had been a moon of Neptune before it was knocked into its own orbit by the impact of Kzanol's ship. Eventually, Greenberg's personality reasserts itself and, armed with the knowledge of how to resist the Power (from Kzanol's own memories), Greenberg traps Kzanol again in a stasis field.
A major element of the story is the Cold War existing between Earth and the "Belters," which threatens to burst into a highly destructive war over control of the telepathic amplifier. The mutually accepted compromise is to throw the spacesuit containing the dangerous device, still in a stasis field, onto Jupiter, where no one can recover it.