As desperation begins to cloud the mind of Scientist Albert Dooley (Dean Jones), he finds himself battling to make ends meet. His wife Katie (Sandy Duncan) embarks on a misguided mission to cut costs, unwittingly setting off a chain of peculiar events that involve a duck named Charley. This unique bird has developed an unexpected taste for irradiated applesauce, and soon becomes the cornerstone of a twist that will transform the Dooleys' lives forever. Initially witnessing this astonishing development are Albert, Katie, their son Jimmy (Lee Montgomery), and Albert’s friend Fred. To their utter astonishment, Charley begins to lay eggs with solid gold yolks.
As word spreads about this miraculous event, the Dooley household turns into a bustling center of excitement and opportunity. They take advantage of their newfound fortune, drawing the ire of their incredulous neighbor, Mr. Hooper (Joe Flynn), an overzealous government bureaucrat from the U.S. Treasury Department. Hooper's clumsy spying antics often lead to humorous situations, including a comical fall from a tree after a stern talking-to from his wife for meddling in the Dooleys' affairs. Nevertheless, he remains dedicated to unearthing the truth behind Charley's astonishing golden eggs.
Rumors eventually reach Rutledge (James Gregory), a senior official at the Treasury Department. Initially doubtful, Rutledge becomes a believer after a series of chaotic calls from his colleagues who assert that the Dooleys are hoarding an extraordinary economic treasure. The urgency escalates as even the President gets involved, issuing an ultimatum to capture Charley and restore economic order.
As the pressure mounts, Albert becomes increasingly obsessed with the golden treasure, causing his son Jimmy to feel neglected and forgotten. In a desperate bid to safeguard their cherished pet, the Dooleys find themselves in a gripping confrontation with the authorities. This culminates in a hair-raising escape, with Jimmy and Charley attempting to evade the clutches of Treasury officials.
During the suspenseful climax, Jimmy precariously balances on a rickety ladder spanning two parking garages, while Albert desperately encourages him to reach out for his hand just as the fragile structure threatens to collapse. At first, Jimmy hesitates, believing his father's true desire lies in saving Charley rather than him. However, as the ladder wobbles perilously, Jimmy’s apprehension gives way to the realization of Albert's selfless intentions. In a tense moment, Albert manages to rescue his son just as the ladder fails, narrowly escaping disaster.
In the aftermath, Albert unexpectedly faces arrest for possessing gold as an individual, a shocking turn of events that stuns the entire family. Things reach a crescendo in a courtroom scene where they encounter a judge who, in a bizarre display of judicial theatrics, attempts to elicit an egg-laying response from Charley through exaggerated quacks. The goofy mimicry of Mr. Hooper proves fruitless, while Albert's surprisingly effective dog impressions result in a mundane egg yolk — a testament to the fading magic of the radiation.
Ultimately, as the charges dissolve due to insufficient evidence for the legendary golden eggs, Albert ponders the entire experience. He recognizes that, although the lure of wealth was captivating, the safety and happiness of his family hold greater significance than any material gain. The judge leaves Jimmy with a playful warning: > "Should that duck ever lay another golden egg...bury it quick!"
