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One afternoon, as animal behaviorist Prof. Albert Dooley contemplates a stack of unpaid bills, his young son Jimmy interrupts to ask if he can buy a puppy. Albert explains to the boy that they cannot afford a pet, and Jimmy sadly declares that Albert is no longer his pal. When Albert then confronts his scatterbrained wife Katie about her expenditures, she proudly presents her homemade applesauce, which is part of her efforts to reduce their food bills. Although Albert is barely able to swallow Katie's garlic-laced concoction, he cannot resist her endearing offer to pack his lunch every day. The next morning, Albert accepts Katie's lunch, then picks up his best friend, lawyer Fred Hines, who laments his own financial plight. At his laboratory, Albert throws away his lunch, greets the animals whose I.Q. he is testing and warns a duck that if she fails her tests again, Albert's boss, Dr. Gottlieb, will remove her from the program. A chimpanzee grabs Albert's lunch but upon tasting the dreadful applesauce, tosses it aside, where it is gobbled up by the duck. Amazed that the animal enjoys it, Albert takes her to the testing room where Gottlieb places her in the simplest device, upon which she has already practiced. The duck fails to pick the correct switch, but when she flips a switch that plays a recording of a barking dog, she lays an egg. Although Albert tries to convince Gottlieb that they should study the duck's reaction, Gottlieb orders the animal removed. While the scientists are wrangling, the duck waddles into the nearby radiology department, where she is accidentally irradiated. To prevent the duck from being destroyed, Albert takes her home, with the intention of giving her to local farmer Purdham. Jimmy is at first dismayed by the duck but, discovering that she likes to follow him, names her Charley, not knowing that she is a girl. Later, after a distressing encounter with the golden retriever belonging to Treasury Dept. agent Finley Hooper, the Dooleys' irritable neighbor, the Dooleys discover that when the dog barks, Charley lays eggs. Despite Katie and Jimmy's amusement at the feat, Albert insists that the eggs cannot be eaten due to the danger of radiation poisoning. Late that night, when Albert begins to bury the eggs, he discovers that the yolks are a gold-colored metal. In the morning, Albert questions Gottlieb about the possibility of radiation changing the molecular structure of an organic substance into an inorganic one, and the older scientist, unaware that Albert's question is not hypothetical, reveals that such experiments have been successful. Albert then gets the yolks tested and the assayer tells him that they are almost pure gold, but with several odd impurities, such as apple pectin, garlic and an unidentifiable component. Believing that his financial woes are solved, Albert tells a skeptical Fred the news. When they arrive home, however, they discover that Katie, not knowing about the gold, has given Charley to Purdham. The family rushes to the farm and after Purdham agrees to sell the duck back to them, are confronted by the sight of hundreds of identical-looking ducks. As the adults search for Charley, Jimmy walks away, followed by a lone duck. Realizing that the animal is his pet, Jimmy yells delightedly. Albert then demonstrates to Katie and Fred that by barking at the right pitch, he can get Charley to lay a gold egg. At home, the adults calculate that each yolk is worth $900, but Fred warns the Dooleys not to spend any money yet, as they must not draw attention to themselves until he can protect their investment. The next day, Katie receives a phone call from banker Meeker, who tells her that her account is overdrawn yet again, and Katie attempts to deposit one of the eggs. The manager tells her that the bank cannot accept gold and that she must take it to a refinery, which she then does. Albert and Fred are horrified upon learning of Katie's actions, especially as Fred has determined that by having the illicit gold, they are breaking federal gold regulations. Upon reflection, however, the men decide that the best course of action is to get rid of the gold by having the innocent-looking Katie take the eggs to various refineries. Although refinery officials laugh at Katie's explanation about the gold's source, they are suspicious enough to report her to the Treasury Dept. After receiving numerous calls, agent Rutledge convenes a task force, which includes Hooper, and theorizes that an underworld gang is manufacturing synthetic gold. Upon hearing the aliases that Katie has been using, however, all of which give her real surname, Hooper realizes that his neighbors are the "gang" they are hunting. While spying on the Dooleys, Hooper sees Albert bark at the duck until she lays a golden egg, and later, attempts to trick Jimmy into giving him one of Charley's eggs. Before Hooper can crack it, however, Katie grabs both the egg and Jimmy, who is still unaware of his pet's unusual ability. When Katie informs Albert about Hooper's subterfuge, he summons Fred and the men rush home. Meanwhile, Hooper has called Rutledge, who decides to confiscate the duck. The government men present their warrant to the Dooleys, but as the adults argue downstairs, Jimmy hears and, fearing for Charley's safety, climbs out the window with her. Taking a bike from Hooper's garage, Jimmy rides off, followed by the grownups. Jimmy eludes his pursuers and reaches the center of town, where he hitches a ride with teenage hot-rod enthusiasts Arvin and Orlo Wadlow. While the government men continue to give chase, Fred, Katie and Albert are forced to abandon their car, which has been wrecked in the pursuit. As Albert takes off on foot, Fred and Katie steal a telephone company truck, then pick up Albert, who climbs into the basket at the back. Fred accidentally hits the control that lifts the basket high into the air, and although Albert's vantage point helps them track the boys, he is in constant danger from tall obstacles. After a wild chase, the boys stop on the roof of a parking garage. They set up a ladder found in the garage to reach the roof of a nearby building, but as Jimmy crosses while holding onto Charley, the ladder slips down a floor. Albert succeeds in rescuing his terrified son and the duck, which is confiscated by Rutledge. Albert is also arrested for violating federal gold regulations, and soon after, at the trial, Hooper testifies about Charley's capabilities. Although Fred urges him to remain silent, Albert realizes that the most important thing in his life is his family and tells the judge that he can make Charley lay the gold eggs. When Albert barks at her, however, Charley lays only an ordinary egg, as the half-life of her radiation poisoning has passed, thereby rendering her incapable of producing gold. The judge dismisses the case for lack of evidence, then ruefully declares that after Albert pays his income tax on his $40,000 fortune, he will have little left. Triumphantly returning Charley to Jimmy, Albert states that the duck still has great value, then walks with his family to greet the cheering crowd outside.