What can go up a chimney down, but not down a chimney up?

How to think about it

1. Separate the two meanings. “Up a chimney” and “down a chimney” are directions; the trailing “down” and “up” describe the state of the object.
2. So the question is: what fits through a chimney while it is “down” but not while it is “up”?
3. Something that is narrow when down and wide when up. Think of something that opens.
4. A closed umbrella slides up a chimney; an open one is far too wide to come down.

Why “an umbrella” is the answer

An umbrella that is “down”, meaning closed, is a thin stick that could pass up a chimney, but an umbrella that is “up”, meaning open, is a wide canopy that could never fit down one. The riddle hides this by using the same two words for direction and for the umbrella’s state. Reading it slowly is most of the solution.

Common wrong answers

• Smoke. Smoke goes up a chimney but the riddle’s “down” and “up” describe the object, and smoke is never up or down in that sense.
• Santa Claus. A fun guess, but he famously comes down the chimney, and he does not fold.