While browsing a flea market, Tintin comes across and buys an old model ship, thinking it would make a good present for Captain Haddock. He is immediately approached by two men who both want to buy it back from him, though Tintin adamantly refuses. One of them even follows him to his home and gives Tintin his business card, which lists him as "Ivan Sakharine, Collector". Tintin once again refuses and sends him on his way but unfortunately Snowy knocks the model over during this distraction, breaking the ship's main mast.
Haddock arrives and Tintin shows his the ship. The former is incredibly surprised and he takes Tintin to his house to show him why: a portrait of his IdenticalAncestor, Sir Francis Haddock, with the exact same ship in the background. Tintin notices the name ''Unicorn'' on the ship's hull and returns home to check if the model has it as well. However, he returns to find the model gone. He immediately suspects Sakharine and runs off to confront him. Tintin's suspicions are apparently confirmed when he finds the model in Sakharine's home but the latter claims he had owned it for over ten years: the reason why he wanted Tintin's model so badly is because he thought it was odd that two identical models existed. Tintin confirms this is not his model since the main mast is still intact as well as that the name ''Unicorn'' is on the hull as well. Tintin returns home and finds the place completely ransacked yet with nothing missing, meaning the intruders were looking for something in particular.
While cleaning up the mess, Tintin finds a small piece of parchment with a cryptic message and some numbers. Tintin concludes that it must have been lodged under the broken mast and that this parchement must be what both his flat's intruders were seeking. Tintin puts the parchment in his wallet and runs off to talk to Haddock and finds him wearing Sir Francis' hat and cutlass: Haddock had gone over his ancestor's sea chest and found these items along with his diary, detailing the story of the ''Unicorn'':
In the year 1676, the Unicorn had left Barbados to set sail for home when it was intercepted by pirate ship captained by the ruthless Red Rackham. After a fierce battle, Haddock finds himself captured and the sole survivor of the ''Unicorn's'' crew. Since his pirate ship is heavily damaged, Rackham orders all of its cargo to be loaded onto the ''Unicorn'', including a chest full of precious gems plundered off a Spanish ship. While the pirates get drunk during the night, Haddock slips away and lights a fuse to the powder kegs in the hold, though he is interrupted by Rackham himself. After a tense battle, Haddock kills Rackham and escapes just in time to escape the explosion. Haddock made his way back home and built three identical models of the ''Unicorn'', each bequeathed to his three sons. According to the diary, if the mast of each is moved, "the truth will come out". Tintin concludes that the parchment he found is what Haddock meant and that it's one of the three keys to finding Red Rackham's treasure. Unfortunately he then notices that his wallet was stolen (Tintin's having the worst day). Tintin and Haddock then make their way to Sakharine's place to look at the second parchment and find him chloroformed on the floor, the mast of his model broken and the parchment gone: clearly Tintin and Haddock are not the only ones looking for the treasure.
Tintin and Haddock return to the former's home and find the other man who tried to buy the model off of Tintin waiting for them, wishing to speak to Tintin. However, a car then does a drive-by and the man is repeatedly shot. Before falling unconscious he says "Be careful...they will kill you too..." while pointing at...some sparrows.
After receiving news that the man is still alive but in a coma, Tintin is contacted by Thompson and Thomson who have recovered his wallet with the parchement, which had been stolen by a pickpocket that had been causing quite the ruckus recently (though he managed to escape). The joy is shortlived, however, as Tintin is chloroformed and kidnapped. He awakens in a cellar where a voice on a speaker accuses him of having stolen two of the parchments. Tintin of course denies this but is disbelieved. Tintin manages to escape and finds a letter explaining why the wounded man pointed at the sparrows: he is in Marlinspike Hall, the home of Gustav and Max ''Bird''. Tintin manages to call Haddock with his whereabouts though he is eventually interrupted by the Bird brothers' butler Nestor. Tintin escapes again and manages to evade the Bird brothers and Nestor long enough for Haddock and the Thompsons to arrive. Max manages to escape but Gustav is cornered, who proceeds to reveal everything: the Bird brothers found the third ''Unicorn'' model after purchasing Marlinspike and found the parchment while restoring the former. They concluded it was the key to a treasure and used their contacts as antique dealers to find the other two. The wounded man, Barnaby, was one of their spies and was also the one who ransacked Tintin's apartment twice to find his parchment. Unsuccessful, he then stole Sakharine's parchment. However, Barnaby then got into a disagreement over his payment and then went to Tintin to spill the beans, prompting the drive-by shooting. The Bird brothers' two parchments were then stolen, which prompted them to kidnap Tintin, believing him responsible. The Thompsons then take Tintin to finally arrest the pickpocket, Aristides Silk. In Silk's impressive wallet collection, Tintin finds the parchments stolen from the Bird brothers and later on Max is captured along side Tintin's parchment, giving the latter access to all three.
All three parchments, when placed on top of each other and facing the light provide a latitude and longitude: obviously the location where the ''Unicorn'' sank. Tintin and Haddock plan to find the treasure, a quest detailed in the second part of the story, ''[[Recap/TintinRedRackhamsTreasure Red Rackham's Treasure]]''.
Hergé once cited it as his personal favourite Tintin story, though he would later come to prefer ''[[Recap/TintinTintinInTibet Tintin in Tibet]]''. Along with ''[[Recap/TintinTheCrabWithTheGoldenClaws The Crab with the Golden Claws]]'', it is the basis for most of the plot of Creator/StevenSpielberg's [[Film/TheAdventuresOfTintin 2011 film adaptation]].
* BerserkButton: Haddock does ''not'' take it well when Thomson and Thompson accuse him of murdering Mr. Sakharine.
* BigBad: The Bird brothers.
* BigDamnHeroes: Snowy, Haddock and the Thom(p)sons arrive in the nick of time to save Tintin when he's being held at gunpoint by the Bird brothers.
* ChekhovsGunman / ChekhovsGag: Aristides Silk the pickpocket becomes vital to the plot when he [[spoiler:steals Max Bird's wallet, containing the last remaining parchment]].
* ClearMyName: A very brief example when the Thom(p)sons accuse Haddock of murdering Sakharine. In truth Sakharine isn't even really dead and Haddock had nothing to do with the attack on him.
* CoolShip: The ''Unicorn''.
* DismantledMacGuffin: The three parchments each containing a part of the coordinates of the sunken ''Unicorn''.
* DyingClue: Barnaby is too weak to speak after being shot, but he points at a nearby flock of sparrows before passing out. He was, of course, hired by the ''Bird'' brothers.
* VillainExitStageLeft: One of the Bird brothers escapes, but Tintin got his car's license plate number and the Twins were able to arrest him at the border.
* GottaCatchThemAll: The ''Unicorn'' models and the parchments.
* HisNameIs: Barnaby is shot before he can tell Tintin the name of his employer.
* HufflepuffHouse: Sakharine, more or less. He is the third party that wants the ship model, though he doesn't seemingly know about the parchments in them.
* IdenticalGrandson: Haddock to his forefather Sir Francis Haddock.
* InformedAbility: Tintin notes that Max Bird is the more dangerous of the Bird brothers at one point. There isn't really much to back this up at that point, and in fact, it's Gustav who held him at gunpoint and almost shot him from behind mere minutes before.
* LeaveNoSurvivors: Red Rackham won't...
* KitschCollection: Silk the pickpocket has a huge collection of stolen wallets, sorted alphabetically. Every single wallet under "T" belongs to the Thom(p)sons!
* RedHerring: Sakharine the ship model collector is accused by Tintin of stealing his model, but he is actually innocent.
* RunningGag: The Thom(p)sons' wallets are stolen almost every time they appear.
* StabTheScorpion: Haddock saves Tintin from Gustav Bird in this manner (with a thrown whiskey bottle).
* StickyFingers: Silk.
* SpannerInTheWorks: Silk the pickpocket, for both Tintin and the Bird brothers.