Gloria Mundy (Goldie Hawn) is attending a party in a town across the bay from San Francisco. From a conversation with a friend we learn that she is recently divorced and is shying away from dating men to avoid getting her heart broken again. Her friend urges her to become more social and for a few seconds she considers getting to know a stranger at the party played by Chevy Chase. Deciding he is a klutz and a bore she drives back to the city alone. As the opening credits roll we see her driving down the gorgeous Marlin County coastline in her yellow VW convertible as Barry Manilow sings the song "Ready to Take a Chance Again."When Gloria passes a handsome stranded stranger with broken down car, she decides to take a chance and pulls over to help. The stranger, Bob Scott (Bruce Solomon) asks her to drive him back to the city. On the way Scott notices that they are being followed by a black limo and decides to slip a cigarette pack, containing a spool of film, into Gloria's purse asking her to meet him at a movie theater later that evening. When she drops him off, we see two men jump from the limo and pursue him.When Scott finally reaches the movie theater, he sits down and we see he is hurt and bleeding badly. He dies shortly after whispering to Gloria "Beware of the dwarf!" She runs from the theater and gets the manager, but by the time they get back to her seat, the body is gone.Gloria tells this story to her elderly landlord Mr. Hennessey (Burgess Meredith), a retired anthropologist who keeps a ten foot snake as a pet, then heads upstairs to go to bed. The next day when she goes to work at the public library she also tells this story to her girlfriend, Stella, (Marilyn Sokol) who is convinced the whole thing is a hoax by a sex-crazed man, and insists the Gloria protect herself by carrying a portable alarm and a can of mace in her purse.As she is closing up the library that evening Gloria finds herself alone with an albino stranger (William Frankfather) who tries to kidnap her. She flees the building with the albino and another swarthy character, The Turk (Ion Teodorescu) in pursuit. Running into a bar she picks up Stanley Tibbets (Dudley Moore) and without telling him whats going on, asks him to take her to his apartment. There, Stanley misreads her intentions and prepares for a wild evening of sex, while she is distracted watching her pursuers out the window. When she finally turns around and sees Stanley in his underwear she is shocked and he is embarrassed. She heads home while Stanley mutters his apologies.Gloria is later assaulted at her apartment by a man with a scar on his face (Don Calfa), who demands she give him whatever was passed to her by Scott. He takes the cigarettes, and then attempts to strangle Gloria, but she stabs him with a pair of knitting needles (The cigarettes fall out of his pocket and lay hidden under a plant). Thinking she has killed him she calls the police, but as she turns around he is up again staggering toward her with murderous intent. The albino suddenly appears at the window and uses a throwing knife to kill the man with the scar and Gloria faints.She awakes to see the face of Chevy Chase's character, who we find is police Lt. Tony Carlson. Gloria tells him her story, but again the body has disappeared. Carlson's partner, Fergie, (Brian Dennehy) thinks she is nuts, but Tony is attracted to her and invites her to the station during her lunch hour.When she leaves the library to meet Tony for lunch she is kidnapped by the albino and the Turk. Waking up locked in a room she uses the portable alarm to get the Turk into the room and then maces him. She then climbs down the fire escape in the pouring rain and jumps to safely. Later she shows up at Tony's office, soaked to the skin and he takes her home.The next day Tony and Fergie check out the room where Gloria was held and find out that it was rented to someone named "Stiltskin." When Tony gets back to police headquarters he is informed that Stiltskin is the name of an assassin whose nickname is the "The Dwarf" and Scott was working undercover trying to find the name of the target. Suddenly Gloria's strange story makes sense and Tony heads out to her apartment to make sure she is okay.In the meanwhile Gloria has a visit from salesman J.J. MacKuen (Billy Barty). As he is a midget, she is terrified and misunderstanding his offer to connect her with eternity pushes him out the window, where he falls into a trash barrel and goes rolling down the hilly San Francisco street. When Tony arrives they open MacKuen's case to find he was an innocent Bible salesman.Gloria, Tony and Fergie head out to the residence of Archbishop Thorncrest, whose limo has been identified as the one used in kidnapping Gloria. The Archbishop (Eugene Roche) and his assistant Delia Darrow (Rachel Roberts), are busy preparing for a visit by the Pope and claim the car has been missing, taken by the chauffer, The Turk. When Gloria and party leave we find out that the Archbishop has been replaced by his identical brother. He and Darrow, Stiltskin, the albino and the Turk are part of an anti-religious conspiracy to kill the Pope.To keep Gloria safe Tony takes her to his house overnight: a fancy houseboat in Sausalito where they become romantically involved. The next day he takes Gloria home where Fergie is supposed to keep an eye on her while Tony heads out to look at where they found scarface's body. Fergie never shows up at Gloria's but she gets a mysterious call from him asking her to meet him at a deserted building next to a "massage" parlor. Stiltskin (Marc Lawrence) and company have kidnapped Fergie and forced him to make the call to trap Gloria. At the last moment Fergie yells a warning and Gloria escapes into the massage parlor hiding in one of the rooms where she again runs into Stanley. Stanley is mortified, but Gloria begs him to call the police and have the house raided. He finally does this, but Gloria is captured anyway while Stanley is hauled off to the police station.When Gloria and Fergie disappear, Tony decides to search the Archbishop's house with the help of Mr. Hennessey. Tony finds Fergie in the basement and a fight erupts between him and Stiltskin were Stiltskin is killed. Tony is captured and taken upstairs where he is tied up with Gloria. The archbishop imposter informs them that even with Stilskin dead, the albino, the backup assassin, will do the job by shooting the Pope from one of the organ bays during that evening's opera. Mr. Hennessey suddenly attacks and the archbishop imposter is knocked cold as a martial arts contest unfolds between the elderly Hennessey and the middle-aged Delia Darrow with the tied up Tony and Gloria watching. Hennessey finally wins and Tony and Gloria are released to make a hair raising race across the city (wrecking several vehicles in the process) to the opera house.They check the first organ bay and it seems empty, so Tony leaves Gloria there while he and the other police leave to check the other side. The albino comes out from where he has been hiding, however, and kidnaps Gloria, dragging her up into the catwalks above the stage while the opera continues below. The albino manages to shoot a pursuing policeman who tumbles over the edge and gets caught in the rigging of a sailing ship "flying" setpiece in the rafters of the theater. The albino is then shot by Tony, falls and is caught in the same way. The set suddenly drops down out of the ceiling at the end of the opera with the two dead men caught in the rigging. The whole theater sits in shock at this until the Pope, apparently thinking this is the way the opera is supposed to end, starts clapping and everybody else joins in. Tony and Gloria find each other and embrace while the crowd cheers. Down the orchestra pit we see the conductor is Stanley, who blanches at seeing Gloria, and slips on a pair of sunglasses hoping to avoid another embarrassing encounter with her.