Susan gazed out the window of the train, the grimy panes distorting her view of the nature flowing past outside. Sighing, she longed for beauty in her life, beauty that she had never known...
Her tiresome introspection was interrupted as the scoutship of the 3rd Imperial Galaxon Fleet landed on the tracks ahead of the train, causing the engineer to pull on the emergency brakes. Havoc ensued inside, as passangers and packages were thrown about in havoc. Fortunately, Lt. Dan "Dangerous" Lloyd, arriving through the wormhole from the 31st century, was there...
Dan gazed upon the scene, and sighed, realizing the futility of armed conflict, seeing history repeat itself yet again. And as he looked into the tired eyes of the Galaxons streaming from the scoutship, send on yet another endless task of conquest, he saw that they too were weary of the conflict...
Then, Ogar, the Giant of the North, stepped on all of them. Ogar then retreated into the night, leaving behind only sorrow. Sorrow, and a thirst for vengeance, which could only be sated by Canan, the Warrior!
A chain story is a story written by multiple authors, each writing a short section (typically a few paragraphs, or pages), and then handing the story off to the next writer.
Depending on the writers involved, and the circumstances of the collaboration, the results can vary wildly. Given as writing assignments in school, the results could be like the example above, with each author disagreeing on the direction of the story, and writing out the characters and plot the others introduce.
However, with a group of people who are willing to try, the excercise can be very rewarding, as each author works with the plot and characters introduced by the others, and adds their own unique touch.
Without any sort of agreed-on plan, a chain story might not go very far, because with such small segments per author, deeper plot and significance is hard to develop. However, as an excercise in creativity, and as an interesting long-term group project (made easier by internet access, mind), it can be quite fun.
And no, the above example was never an actual chain story, thank goodness