Frustrated by his stagnant, unchallenging, mid-level job as a computer programmer, Webster McGee decides to quit the Houston Control Data Corporation and live the more exciting life of a jewel thief. After arranging a partnership with fences Deams and former prizefighter Dynamite Hector, Webster uses his inside information of wealthy businessman Gene Henderling and applies his computer knowledge to break through the high security system at the Henderling mansion while they are on vacation. Along with the Henderling jewels, Webster puckishly steals the gold and silver chess set and leaves a note with an opening game move, resulting in the press dubbing the theft the “Chess Robbery.” Confronting Henderling soon afterward, Webster informs him that he is the thief and, revealing that he has evidence of a major fraud conducted by the magnate, blackmails him into extending an invitation to a private party of Houston’s high society. At the party, Henderling introduces Webster to several wealthy associates, including the beautiful Laura Keaton. Immediately attracted to Webster, Laura is nevertheless skeptical of his revelation that he is a jewel thief but allows him to drive her to her large but mostly unfurnished home. Admitting that she inherited the house, which remains in trust, from her father, Laura reveals she cannot afford to maintain the property, so lives there in stark fashion. Fascinated by Webster’s description of robbery as an exhilarating experience, Laura agrees to help on his next caper. After Webster settles on the wealthy Slaters as his next victims, Laura invites them to a charity costume ball she is hosting, assuring that their house will be vacant when Webster comes to rob it. Distracting the Slaters’ guard dogs with a female dog in heat, Webster breaks in easily and leaves another chess move note before fleeing in a sports car provided by Dynamite. On driving away, however, Webster is rear-ended by an old lady and when the police stop to help, Webster panics and races away. A frantic chase ensues, with Webster arriving on foot to Laura’s costume ball in time to provide himself an alibi. A few days later, Texas Mutual Insurance investigator Dave Reilly visits Laura to request a guest list for the ball. Having moved in with Laura, Webster insists that she provide the list and cheerfully asks Reilly about his investigation. Knowing the thief must have a fence, Reilly begins watching Dynamite, then soon after convinces the Houston newspaper’s chess columnist, Zukovsky, to challenge the thief to a public chess match to be dubbed the Chess Burglar Challenge. Delighted by the competition, Webster breaks into his former office and runs a program he had designed featuring the best moves of established chess masters from around the world. Over the next several weeks, Webster conducts several successful burglaries of Houston’s elite and gradually frustrates Zukovsky with the chess moves he leaves behind. Reilly telephones Webster for a meeting and he agrees on the condition that the insurance investigator accompanies him on his daily jog. During the run, Reilly discloses that he has questioned each guest at the charity ball and concluded that the only one who does not fit in with the crowd is Webster. Urging Reilly to arrest him if he truly believes he is the thief, Webster laughs when Reilly admits he has no evidence. After the unexpectedly grueling jog puts Reilly temporarily in the hospital, he is surprised when Webster pays him a visit with a gift of the book Don Quixote , a man, Webster reminds the investigator, who did not believe in reality. Upon his release, Reilly continues pursuing Webster, blatantly following him regularly. Flustered, however, when Webster readily acknowledges his presence and even comes to his aid when his car stalls, Reilly remains unable to link Webster to the robberies. Soon after, Laura meets Webster at his apartment where he gathers a change of clothes and reveals she answered his phone and took a message from his ex-wife, actress Jackie Johnson, who will be in Houston soon performing in a play. Dismissing Laura’s anxiety, Webster assures her that he loves her. After Jackie arrives in Houston, Reilly visits her after her first performance, but she is incredulous that Webster, whom, despite his good looks, she thught of as dull and boring, could be the infamous Chess Burglar. When Jackie visits Webster later, she is amazed when he admits to being the thief, but when she suggests they resume their relationship he refuses, revealing he loves Laura. After Reilly meets Henderling to suggest that he is Webster’s contact into Houston’s wealthy set, he later follows the panicked businessman to Laura’s house. There, Webster reassures Henderling that Reilly has no substantial information or he would not have confronted him in that way. Soon after, Webster and Laura attend a museum’s private viewing of a new exhibition featuring a lavish diamond. Later, Webster meets with Deams to ask him to prepare for their largest “drop” which should bring in over a million dollars. While Laura resumes flying lessons she had taken earlier, Webster, disguised as a priest, rents a secluded lakeside property. The day after arranging for the property, Webster, still dressed as a priest, goes to the museum shortly before closing, sneaks down to the lower level and chloroforms the guard overseeing the security monitors. After the museum is officially closed, Webster sneaks back upstairs, knocks out two other guards and, using a laser tool, cuts through the glass case around the diamond and takes it. As he is sneaking out on the lower level, however, the guard revives and in the ensuring fight, Webster is shot in the arm before making his escape. Meeting Laura at the lakeside cottage, where she is waiting for him with a water plane, the pair fly to the Gulf of Mexico and meet Deams and Dynamite on board the yacht of wealthy Señor Rivera, who happily buys the diamond for one million dollars in cash. Returning to Houston, Laura treats Webster's wound and the next day Reilly stops by. Excited by the report that the Chess Burglar had been wounded at the museum heist, Reilly fully expects to find Webster in bed and is dismayed when Webster arrives from a jog and invites him to come along. Dismayed, Reilly departs just before Webster collapses. At the newspaper, Zukovsky receives the burglar's chess move from the museum robbery, which is a check-mate. At the insurance office, Reilly is dismayed when his boss informs him he is being replaced on the burglary case as he has spent all his time on Webster without success. Quitting in outrage, Reilly nevertheless continues following Webster. A few days later, when Webster breaks into a luxury-item store to steal the window display of a gold and silver chess set, Reilly is waiting for him. After Reilly rings the alarm to summon the police, Webster tells him that jail does not suit his lifestyle and wonders if Reilly has grown as fond of him as Webster has of Reilly. When Webster then turns and walks away, Reilly lets him go.