The "Number One Dime" is an object owned by Scrooge McDuck. It is the first Dime he ever earned in 1877, when he worked as a shoe shiner in Glasgow.
During the theme song, Scrooge, his family and his enemies are all chasing the Dime. Scrooge keeps the Dime on a chain in his neck. He keeps another dime exhibited on a pillow in a money bin as a decoy. In "The Great Dime Chase!", Louie Duck accidentally spends the decoy dime on a can of soda and spends the entire episode trying to get it back, believing it's the actual Number One Dime.
Fifteen years prior to the show's events, Magica De Spell attempted to get the Number One Dime and lock Scrooge inside it, but Scrooge managed to invert the spell, locking Magica in the Dime instead. In "The Shadow War!", Magica succeeds in freeing herself from the Dime and imprisoning Scrooge in it.