The song “Cheek to Cheek” (1935) by Irving Berlin (1888-1989) popularized “dancing cheek-to-cheek.” A riddle is:
 
Q: How do cjhickens dance?
A: Chick to chick.
 
The riddle has been cited in print since at least 1975.
 
“Dancing cheek-to-cheek is really a form of floor play” is a related pun.
       
 
Google Books
Wild Bill Hiccup’s Riddle Book
By Ann Bishop and Jerry Warshaw
Chicago, IL: A. Whitman
1975
Pg. ?:
How do hens and roosters dance?
Chick to chick.
   
3 September 1982, The Times-Picayune & The States-Item (New Orleans, LA), Lagniappe, pg. 15, col. 1:
Q. When the band plays what do chickens do?
A. Dance chick to chick.
Renea Kupper, age 9
 
Google Books
The Last Official Smart Kids Joke Book
By Larry Wilde
New York, NY: Bantam Books
1983
Pg. 32:
“How do baby chickens dance?”
“Chick to chick, naturally.”
 
Google Books
The Zaniest Riddle Book in the World
By Joseph Rosenbloom
Illustrated by Sandy Hoffman
New york, NY: Sterling Publishing Company, Inc.
1984
Pg. 35:
How do chickens dance?
Chick-to-chick.
   
14 August 1988, Newsday (Long Island, NY), “Smiles,” Kidsday sec., pg. 1:
How do baby chickens like to dance?
Chick-to-chick.
- Nancy Stern, Farmingville
 
7 January 1993, Vancouver (BC) Sun, “You’ll have fun making friends with these bright yard birds,” pg. C10:
Q: How do chickens dance?
A: Chick to chick.
 
Google Books
A Prairie Home Companion
Pretty Good Joke Book
Introduced by Garrison Keillor
Prince Frederick, MD: HighBridge, a division of Recorded Books
2015
Pg. ?:
How do chickens dance?
Chick to chick.
 
Twitter
Puns of Jokes‏
@punsofjokes
How do chickens dance? Chick to chick.      #rotf #punny
3:16 PM - 19 Apr 2017