The film opens with a knife attack upon the
Archbishop of San Francisco (Eugene Roche), perpetrated by a man identical to the Archbishop in looks and dress. We are then introduced to Gloria Mundy (Goldie Hawn), who is recovering from a recent divorce. She decides to pick up an attractive man (Bruce Solomon) whose car has broken down and the two agree to go to the movies in the evening. As the man leaves the car, he is chased by two men getting out of a
limousine, one of them an
albino. Later at the cinema, the hitchhiker warns Gloria to "beware of the
dwarf" and dies from a gun shot wound (apparently received in the earlier chase). As Gloria runs out, the dead body strangely disappears, and hence nobody believes her. The next day, Gloria is attacked at the library she works at by the Albino but manages to escape with the help of Stanley (Dudley Moore) whom she picked up at a bar and who thinks she is interested in having sex with him. Finally arriving at her home, she is surprised by a man with a scar (Don Calfa) who demands the cigarette packet the hitch hiker gave her.(The audience sees that it contains a roll of film but also that it drops into a shrub.) Scarface tries to kill her but is stopped by the sudden appearance of the Albino, who kills Scarface. Gloria fades out and as she wakes up, all traces of these events, including the dead body of Scarface are gone. She incoherently tries to explain what happened to the two police officers, Fergy (Brian Dennehy) and Tony (Chevy Chase), and her landlord, Mr Hennessy (Burgess Meredith) but none of them believe her. The next day, Gloria is abducted by the limousine's chauffeur and the Albino but later manages to escape and is taken home by Tony, who is clearly romantically interested in her. In his inquiries. Tony comes across a contract killer nicknamed the Dwarf (Marc Lawrence) and finds out that a recently murdered detective, the hitch-hiker, was on his trail. He is then assigned to protect Gloria from her would-be assassins. Finding out that the limousine is registered by Archdiocese of San Francisco, the detectives and Gloria pay a visit to the Archbishop (actually his replacement seen in the first scene), who informs them that the car has been stolen by the chauffeur called Turk. After the detectives have left, we see the Albino, Turk and the Dwarf all assembled together with the Archbishop and his housekeeper (Rachel Roberts). Gloria and Tony spend the night together. The next day, the Dwarf kidnaps Fergy (who is assigned to protect Gloria) and uses him to lure her into a trap. At first, she manages to hide in a
massage parlor, where she runs into Stanley again, but then is found and abducted by the Albino and the Dwarf. As Turk belonged to a group called
Tax the churches league, Gloria had her library friends do research on them; the group had tried to kidnap
Billy Graham in the
1960s and a photo shows its leader Delia Darrow, who looks just like the Archbishop's housekeeper. Tony and Mr Hennessy go to the Archbishop's residence again. Tony finds Fergy, who informs him that the Dwarf is hired to assassinate the visiting
Pope Pius XIII at this night's
opera performance. Tony is attacked by the Dwarf and kills him in self-defence, but is forced to surrender to Delia Darrow. She and the fake Archbishop (actually the bishop's estranged twin brother) lecture them on their motives and inform them that the plan would go ahead, with the Albino replacing the Dwarf. They are surprised by Mr Hennessy, who knocks out the fake Archbishop and defeats Delia Darrow in a pseudo-
martial arts duel. In a typical
San Francisco car chase, Gloria and Tony rush to the opera house, where Gloria runs into the Albino. He takes her back stage and kills a pursuing policeman but is himself shot by Tony. Both dead bodies, entangled in the one of the
props, are lowered unto the stage, causing momentary shock and embarrassment. This is broken up by the Pope's applause into which all join in. The curtain falls and Gloria and Tony are united in a kiss, not noticing as the curtains are lifted again. Finally, they and the opera cast bow to the applauding audience.