Miss Marple accompanies Virginia Revel to a weekend party at her family home of Chimneys — a house once prized for its diplomatic gatherings until a diamond was stolen there more than twenty years ago.
The tenacious career politician, George Lomax, has persuaded Virginia's father, Lord Caterham, to host a gathering for an important Austrian Count, Ludwig von Stainach. Virginia, who is the daughter of Miss Marple's late cousin, must decide by the end of the weekend whether to accept Lomax's proposal of marriage or to follow her heart and the courtship of another more adventurous suitor, Anthony Cade.
Lomax is dismayed by the odd array of guests who have been invited and castigates his affable assistant Bill Eversleigh, who also has a soft spot for Virginia. Along with Miss Marple there is nosy Miss Blenkinsopp and Caterham's formidable eldest daughter Bundle as well as the quietly inscrutable maid Treadwell.
Count Ludwig takes a personal interest in Chimneys and after dinner Caterham entertains discussions about the sale of the house and a deal is drawn up. But in the middle of the night the guests are stirred from their beds by security and the Count cannot be found. The sound of a gunshot is heard from a secret passageway in the house and Count Ludwig is found dead in the arms of Anthony Cade. Why is Cade at Chimneys — is Virginia's suitor being framed for murder?
A Chief Inspector arrives from Scotland Yard to investigate, taking Miss Marple under his wing and together they discover a coded message in the pocket of the dead Count which could unlock the mystery. But soon enough Miss Marple realizes that the secret of Chimneys is darker than even she had imagined.
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"Chimneys" is a sprawling manor house, notable for its abundance of...chimneys. Aside from a diamond heist at a party in 1932 — obviously the work of the parlor maid Agnes, who absconded — the stately home seems the perfect setting for official government negotiations regarding Austrian iron ore in 1955.
Acting for British interests is Member of Parliament George Lomax, the prospective son-in-law of Chimneys' owner, the Earl of Caterham. Caterham's daughter Virginia is lukewarm to George and more keen to marry Anthony Cade, a handsome young man who rescued her from a mugging on the streets of London.
Representing Austrian interests is Count Ludwig von Stainach, a middle-aged aristocrat with old world charm. He bonds instantly with Chimneys; indeed, he insists on negotiating away mineral rights in exchange for title to the house. He also bonds with Virginia in a fatherly way.
However, before the transfer of the deed is made official, the count is shot dead in a secret passageway beneath the manor house. And who should be next to the murder weapon, grasping the dying count, but Anthony!
Arriving to investigate, Inspector Finch takes Anthony into custody and tells everyone else not to leave as he begins to unravel the mystery — with much help from Miss Marple, who is a house guest and an old friend of Caterham's late wife.
As usual, there are no end of motives. Virginia's sister, Bundle, is so attached to Chimneys that homicide seems logical in order to keep the house from falling into the count's hands. Also present is Hilda Blenkinsopp, a preservation enthusiast who desperately wants Chimneys as a National Heritage tourist attraction.
And behaving very strangely is Treadwell, the long-serving housekeeper, who knows undisclosed details about the 1932 party. When Miss Marple notices in an old photo that the count was present at that very event — as a musician for the orchestra — Treadwell reveals that she saw a light that night and followed it to a crypt, where she glimpsed the body of Agnes, the parlor maid who allegedly stole a guest's diamond. At the crypt, the inspector, Miss Marple, and Caterham discover Agnes's long-decayed corpse. Not long after, Treadwell is found murdered with poison.
Believing that the count stole the diamond and murdered Agnes in 1932 because she knew of the theft; and that Anthony killed the count while looking for the gem, Inspector Finch officially arrests Anthony for murder. The accused briefly escapes to the hidden passage, where in a frenzy he makes a racket. Greatly muffled from the house, the disturbance convinces Miss Marple that Anthony must be innocent, since the loud "shot," heard by all the night of the count's murder could not possibly have come from the passageway. It was, she realizes, a fireworks explosion set off nearby, meant to create the impression that the shooting had taken place later than it did. The shooter? Caterham.
Putting two and two together, Miss Marple surmises that during the 1932 party, Caterham caught his wife in an assignation with the musician (later known as the count). Trying to prevent the discovery, Agnes was accidentally killed by Caterham. In a quick-thinking cover-up, Caterham stole the diamond from a sleeping guest and placed it with Agnes's body in an empty crypt. (Caterham later surreptitiously removed the jewel when he opened the crypt for Inspector Finch.)
Twenty-three years later, when Caterham was shown the count's letter about the upcoming meeting at Chimneys, he recognized the musician's handwriting and laid plans to kill him, conveniently seizing on Anthony's secret arrival to see Virginia as an opportunity to frame the young man for the count's murder. Caterham later poisoned Treadwell out of fear she would reveal his wife's relationship with the count.
In a surprising development, Virginia turns out to be the count's daughter, conceived at that memorable 1932 party. Virginia and Anthony get engaged, and the final loose end — the future of Chimneys — is tied up when Hilda gratefully accepts the house for National Heritage. It will make a very interesting tourist attraction indeed!