A chimney riddle is:
   
Q: What did the big chimney say to the little chimney?
A: “You’re too young to smoke.”
 
The (cigarette) smoking joke has been cited in print since at least 1941.
     
     
Newspapers.com
5 October 1941, Miami (FL)

, “Riddles,” pg. 6-D, cols. 5, 6:
What did the big chimney say to the little chimney?
—Sent by Ethel Haines, 12.
You’re too little to be smoking.
 
29 November 1942, Boston (MA) Herald, “Riddles,” pg. B10, cols. 6, 8:
What did the big chimney say to the little chimney?
You’re too little to smoke.
 
3 January 1943, Sunday Times (Chicago, IL), “Riddle Club,” pg. 27-M, cols. 3. 5:
What did the big chimney say to the little chimney?
—Leonard Walz. Chicago.
It said, “You’re too small to smoke!”
 
Google Books
Everybody’s Party Book
By Harry Wright Githens
Franklin, OK: Eldridge Entertainment House
1948
Pg. 24:
What did the big chimney say to the little chimney?
(You’re too little to be smoking.)
 
Google Books
The Lore and Language of Schoolchildren
By Iona Archibald Opie and Peter Opie
Oxford, UK: Clarendon Press
1960
Pg. 82:
What did the big chimney say to the little chimney ? — You’re too young to smoke.
   
Google Books
Children’s Riddling
By John Holmes McDowell
Bloomington, IN: Indiana University Press
1979    
Pg. 250:
30. What did the big chimney say to the little chimney? “You’re too young to smoke.” (boy, 6)
Ainsworth, SFQ 1962, #324.
 
Google Groups: alt.humor.puns
Kids Puns of the Weak 06-08-04
Stan Kegel
6/8/04
(...)
*What did the big chimney say to the little chimney?
You’re too young to smoke!! (Julie, 7)
   
Google Groups: alt.humor.puns
Kids Puns of the Weak 12-21-04
Stan Kegel
12/21/04
(...)
What did the big chimney say to the little chimney?
“Don’t ever smoke!” (Abigail, 11)
   
Reddit—Jokes
Posted by u/denturedocelot December 9, 2015
What did the big chimney say to the little chimney?
You’re too young to smoke.
   
Reddit—AntiJokes
Posted by u/BaronVonPingas January 11, 2017
What did the big chimney say to the little chimney?
I have lung cancer
 
Reddit—Jokes
Posted by u/chozang December 15, 2019
What did the big chimney say to the little chimney?
You’re too young to smoke.
COMMENTS
Pun factory
That one flue right over my head.
Johnatomy
Chute. That was funny.