An alien named Baltazar has set his sights on Earth, planning to compress its population into diamonds. The Tenth Doctor and Martha Jones arrive on his ship to stop him. The Doctor threatens him with a spoon, which Baltazar cuts in half with his metal claw hand. The spoon happens to be made of a special fungus, which when introduced to the metal ship quickly begins to rust it. As the ship falls apart, the Doctor frees Baltazar's huge metallic bird, Caw, who carries Baltazar away. The Doctor muses that Baltazar will end up on the ice prison planet Volag-Noc at some point.
Some time later, Caw takes the Doctor and Martha to his home planet, where he gives Martha a brooch as a gift. He also spits up a datachip, explaining that it and three others like it hold the location of The Infinite, an ancient spaceship that can grant people their heart's desire. Each datachip leads to the next one. At first unwilling to search for it, the Doctor is forced to when Caw notes that Baltazar has a copy of the datachip. As the two set off on their quest, Caw is revealed to be working for Baltazar.
The first chip leads to the planet Boukan, where the pirate captain Kaliko is raiding the living oil rigs they find there. She is wearing the next datachip as an earring. Assuming the Doctor and Martha to be spies for the oil companies, Kaliko tells her crew of skeletons to throw them overboard, unaware that her first mate, Mr. Swabb Mate, is in fact the spy. Swabb stages a mutiny and has the oil rigs shoot down the ship, but their poor aim causes them to scatter the crew in doing so. After Swabb is knocked out, the Doctor reveals the reason for their visit to Kaliko. She tries to escape in a pod, but is found murdered after landing near the TARDIS. With nothing left to do, the Doctor and Martha take her datachip and follow it to the next one.
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