A monster is loose in some setting where you would not expect such a thing to be running about. The Cast must capture it. Important: any RPG party is going to be set up to kill monsters. That's why the mandate is to take the thing alive.
Pros:
This can be used in just about any setting, and its fairly straightforward in terms of plot structure.
Cons:
If the creature is obvious, then local authorities may be complicating things with their own efforts. Also, this gag is only funny so many times.
Fate Value: 1/Core dice of the monster
Example:
"Among the many troubles Missouri has in this year of 1855 is a crack in time, though which you have come, and, yesterday, a Tyrannosaurus Rex passed through. You will capture this dinosaur and bring it back here. The natives are a little on edge, what with the oncoming Civil War and all. Try not to attract attention."