“A guy walks into a bar…” is a typical form of what has been called the “bar joke.” A “chicken or the egg” version is:
     
“A chicken and an egg walk into a bar. The barman says, “Right, who’s first?”
   
The joke has been cited in print since 2011 and appears to have originated on Facebook.
   
   
Wikipedia: Chicken or the egg   
The chicken or the egg causality dilemma is commonly stated as the question, “which came first: the chicken or the egg?” The dilemma stems from the observation that all chickens hatch from eggs and all chicken eggs are laid by chickens.
   
Twitter
Gary Blackman
@GB7698
A chicken and an egg walk into a bar. The barman says “who’s first?”.
4:17 PM · Mar 4, 2011· HTC Peep
   
Twitter
Do you need it?
@Firecul
A chicken and an egg walk into a bar, barman says “Right, who’s first?”
9:34 PM · Mar 4, 2011·TweetDeck
   
Twitter
Wopambana
@BwanaChris
Chicken and an egg walk into a bar. The barman says “Right, who’s first ? “
5:36 AM · Mar 5, 2011·erased734497
   
Twitter
Steven Francis
@CaldyTheSeagull
A chicken and an egg walk into a bar.
The barman says, “Right, who’s first?”
1:20 PM · Mar 5, 2011·Twitter Web Client
     
Twitter
The Poke
@ThePoke
A chicken and an egg walk into a bar. The barman says, “Right, who’s first?” via #fb
3:39 PM · Mar 5, 2011·Twitter Web Client
 
Twitter
Oz Warren
@ozzzie
pokeHQ: A chicken and an egg walk into a bar. The barman says, “Right, who’s first?” via #fb: Oz Warren http://bit.ly/g8HZJl
4:02 PM · Mar 5, 2011·twitterfeed
 
Reddit—Jokes
Posted by u/semester5 July 28, 2015
A chicken and an egg walked into a bar…
Bartender was confused who came first.
     
Facebook
The Trumpets
July 7, 2020 at 4:31 AM ·
Monday’s joke:
A chicken and an egg walk into a bar. 
The bartender says: “Who’s first?”
 
Reddit—Jokes
Posted by u/Doghead45 July 17, 2020
A chicken and an egg walk into a bar
The bartender has his back to them, cleaning a glass. He turns around and sees them both sitting there. “Alright, which one of you came first?”
   
Twitter
Davy Gavin [Flag of Scotland] for freedoms sake.
@DavyGavin1
A chicken and an egg walk into a bar. The barman says,  “Who’s first?”.
6:01 PM · Mar 6, 2021·Twitter for Android
 
Twitter
Robert Wilkinson
@robertwlk
A chicken and an egg walk into a bar.
Barman says; “Who’s first?”
7:17 AM · Jun 2, 2021·Twitter Web App