Nick Halloway (Chevy Chase) is a stock analyst who spends most of his life avoiding responsibility and connections with other people. At his favorite bar, the Academy Club, his friend George Talbot (Michael McKean) introduces him to Alice Monroe (Daryl Hannah), a TV documentary producer. Sharing an instant attraction, Nick and Alice make out in the ladies' room and set a lunch date for Friday.
The following morning, a hungover Nick attends a shareholders' meeting at Magnascopic Laboratories. Unable to endure the droning presentation by Dr. Bernard Wachs (Jim Norton), Nick leaves the room for a nap. A lab technician (Aaron Lustig) accidentally spills his mug of coffee onto a computer console, causing a meltdown, and the entire building is evacuated. The building seems to explode, but there is no debris. Instead, much of the building is rendered invisible, including Nick.
Shady CIA operative David Jenkins (Sam Neill) arrives on the scene, and discovers Nick's condition. While they are transferring him to an ambulance, the agents joke about how Nick will spend the rest of his life being studied by scientists. In a panic, Nick flees. Jenkins convinces his supervisor Warren Singleton (Stephen Tobolowsky) not to notify CIA headquarters so that they can capture and take credit for Nick, who could become the perfect secret agent.
Nick hides at the Academy Club. He locates Dr. Wachs and asks for his help to reverse his condition. Wachs agrees to help, but Jenkins kills him to keep Nick's invisibility a secret. Nick infiltrates the CIA headquarters to find any information that can be used against them. Jenkins discovers Nick and tries to recruit him, but Nick is disgusted by the idea of him killing people. They have a confrontation, but Nick gets away.
Nick goes to San Francisco and stays in George's remote beach house. George arrives with his wife Ellen (Patricia Heaton), Alice, and another friend, to spend the weekend. Nick phones Alice and tells her to meet him nearby. He reveals his condition to Alice, and she promptly faints. When she revives, Alice decides to stay with Nick and help him.
They travel to Mexico, where Nick can start a new life. To make money, he trades stocks using Alice as a proxy. Jenkins tracks them down, and shoots Nick with a tranquilliser gun. Nick falls into a river, revives and escapes. He makes his way to a video store, where he records his memoirs on video tape, including an ultimatum for Jenkins: exchange Alice for the tape, or Nick will give it to the CIA and the press. Jenkins agrees to the exchange.
At the arranged time for the exchange, Jenkins puts Alice into a cab and orders his men to surround the phone booth where he thinks Nick is. The man in the phone booth turns out to be George, who is dressed in Nick's concealing clothing. Nick is disguised as the cab driver; he takes Alice away, pursued by Jenkins. They continue the chase on foot into a building still under construction. At the top, Nick tricks Jenkins into plunging to his death.
Believing Nick to be dead, Singleton releases Alice. Nick reunites with Alice and they leave for Switzerland. The film ends with shots of Nick's apparently empty clothing skiing down a mountainside towards their chalet, where a pregnant Alice greets him with a hot drink and a kiss.
For what organization is David Jenkins an operative of?
CIA