Tintin, a young journalist, and his dog Snowy, are browsing in an outdoor market in a European town. Tintin buys a model of a three-masted sailing ship, the Unicorn, for a good price, but is then immediately accosted by the sinister Ivan Ivanovitch Sakharine, and the mysterious figure of Barnaby, who both try to buy the model from Tintin, without success. Tintin takes the ship home, but it is broken during a fight between Snowy and a neighbour’s cat. As it breaks, a parchment scroll slips out of the ship’s mast. Snowy spots it but is unable to alert Tintin. Meanwhile, incompetent detectives Thomson and Thompson are on the trail of a pickpocket, Aristides Silk. Tintin visits Sakharine in Marlinspike Hall, where he learns that there are at least two model ships.
Later, Tintin is shot at, then abducted by accomplices of Sakharine, and imprisoned on the SS Karaboudjan. On board, Tintin escapes and meets the ship’s nominal captain, Haddock. Haddock has been supplied with whisky by first mate Allan, who is working for Sakharine, and the captain is permanently drunk, and doesn’t know what’s happening on board his ship. Tintin and Haddock (and Snowy) eventually escape from the Karaboudjan in a lifeboat. Sakharine sends a seaplane to find them, but Tintin is able to capture the plane, and fly towards the (fictitious) Moroccan port of Bagghar, but they crash in the desert.
Dehydrated in the heat, and suffering from a sudden lack of alcohol, Haddock hallucinates, and starts to remember stories about his ancestor, Sir Francis Haddock(e), who was captain of the Unicorn during the 17th century. Sir Francis’ treasure-laden ship was attacked by a pirate ship, led by the masked Red Rackham, and, after a fierce battle and eventual surrender, Sir Francis chose to sink the Unicorn, and most of the treasure, rather than allow it to fall into Rackham’s hands. It transpires that there were three models of the Unicorn, each containing a scroll. Together, the scrolls will reveal the location of the sunken Unicorn, and its treasure.
In Bagghar, Tintin and the Captain find out that the third model ship is in the possession of the wealthy Omar Ben Salaad, but it is encased in a bullet-proof glass display case. Sakharine’s plan is to stage a concert involving famous diva Bianca Castafiore, the “Milanese nightingale”, whose penetrating singing voice will be able to shatter the glass case, allowing Sakharine’s trained hawk to fly down and steal the third scroll. After a chase down to the harbour, pursued by Tintin and Haddock, Sakharine finally escapes with all three scrolls. Tintin chases him back to Europe and arranges a police reception for him on the dockside. Haddock and Sakharine, who is revealed to be the descendant of Red Rackham, replay their ancestors’ swashbuckling sword fight, using dockside cranes, and Haddock is eventually victorious.
With the three scrolls in their possession, Tintin and Haddock find that the indicated location is Marlinspike Hall, and that the hall had been built originally by Sir Francis Haddock. There, in the cellar, they find some of the treasure, a clue to the location of the sunken Unicorn, and, perhaps, the excuse for another adventure.