The answer to the riddle, "What can go up a chimney down, but cannot go down a chimney up?" is an umbrella. Obviously, once an umbrella has been opened, it becomes too wide to fit in a narrow chimney.
This particular riddle is featured on level 66 of a popular Android app called Riddle Me That! Each level of the app displays a single riddle and a selection of jumbled letters. Using the available letters, the player must select the correct answer to the riddle. The app offers 160 levels of play, and answers for all levels are available online at sites such as riddlemethatanswers.com.