The question of whether or not A Christmas Carol is based on a true story is answered by the presence of the ghost of Scrooge's former business partner, Marley, as well as Ghost of Christmas Past, the Ghost of Christmas Present, and the Ghost of Christmas Yet to Come. Ghosts are not real, and therefore, this cannot be based on a true story. However, like many of the works of Charles Dickens, parts of the story do serve to create a realistic impression of what England was like at the time and how hard people had to work just to get by.
It quickly becomes apparent to the reader that this cannot be a true story, because soon after Bob Cratchit leaves, the ghost of Marley arrives, terrifying Scrooge and leading to him demanding mercy. Marley gives Scrooge a chilling message, telling him that if he does not change his ways, he will end up like Marley in the afterlife, chains and all.
Rather than being a true story, A Christmas Carol is a story written to provide a lesson about the importance of kindness, generosity, and not cutting oneself off from the world. It is the story of how Scrooge became a better man.