Chickens go “bock bock bock.” A riddle has been cited in print since at least 2006:
 
Q: What is a chicken’s favorite beer?
A: Bock.
 
A Texas riddle (about Shiner Bock from a brewery in Shiner, Texas) has been cited in print since at least 2015 and 2016:
     
Q: What is a Texas chicken’s favorite beer?
A: Shiner Bock Bock Bock!
     
     
Wikipedia: Bock
Bock is a strong beer of German origin, brewed as a lager when made with only barley malt, and brewed as an ale when wheat malt is added.
   
Wikipedia: Spoetzl Brewery
Spoetzl Brewery (originally Shiner Brewing Association) is a brewery located in Shiner, Texas,
(...)
Shiner Bock – Spoetzl’s flagship beer. Bock has been brewed since 1913, almost as long as the Spoetzl Brewery has been in business. However, it was not until a few decades ago that Shiner began producing a bock beer year-round. Shiner Bock was considered a Lenten beer, and therefore was only made around that season. Today 73% of the beer made at the Spoetzl Brewery is bock beer.
           
AnandTech 
What’s a chicken’s favorite kind of beer?
BlancoNino Nov 8, 2006
Bock.
 
Twitter
JESSE SALAZAR
@SalazarSpots
Q: What’s the favorite beer of a Texas chicken? A: Shiner BOCK! http://gif.co/s2Yj.gif
8:29 PM · Nov 18, 2015·Twitter for iPhone
   
Twitter
Hander of the Sass, Giver of the Business.
@TheWorstAmy
What is a chicken’s favorite beer?
Michelob Amber Bock Bock Bock!
Just a little liquor store humor for you.
10:41 PM · Jan 2, 2016·Twitter for Android
   
Twitter
Katie Lauren
@katelrn91
What is a chicken’s favorite beer??  Shiner Bock Bock Bock
7:34 PM · Feb 23, 2016·Twitter for Android
   
Twitter
Cheryl
@4leaffun
What’s this chickens favorite beer? Shiner Bock, bock, bock! #BeerAQuote #NationalBeerDay #ThirstyThursday #ReallifeinRoundtoptexas
10:47 AM · Apr 8, 2018·Twitter for iPad
   
Twitter
Harpovember!
@myopiabillson
What’s a chicken’s favorite beer?
Bock!
Instant Rimshot: http://bit.ly/1eUzUFm
#terriblejester #hourofcute
12:30 PM · Jun 11, 2018·TweetDeck
   
Twitter
Kevin Zelnio
@kzelnio
Guys, what’s a chickens favorite beer? Bock!
7:49 PM · Jul 10, 2018·Twitter for Android
   
Twitter
Sarah Hellesen
@sehelles
Hey guys
What’s a chicken’s favorite beer
...Bock.
7:28 PM · Feb 16, 2019·Twitter for iPhone
 
Reddit—Dadjokes
Posted by u/aerozeppelinn July 24, 2021
What is a chicken’s favorite beer?
Double bock
   
Twitter
Andrew Rose (he/him)
@drewrose85
What’s a chicken’s favorite beer you ask? Bock
6:30 AM · Oct 27, 2021·Twitter for iPhone
 
Reddit—Dadjokes
Posted by u/Seven_Arcadian November 25, 2021
What is a chicken’s favorite beer?
Bock
 
Reddit—Dadjokes
Posted by u/zrrbite November 27, 2021
What is a chickens favorite beer?
Bock.