“Which came first: the chicken or the egg?” is a classic question. “Which came first, the chicken salad or the egg salad sandwich?” was asked in Ladies’ Home Journal in May 1975. “Then there was the philosopher who went into a restaurant and ordered an egg salad sandwich and a chicken salad sandwich. He wanted to find out which one came first” was printed in Boys’ Life in October 1981.
 
Newspaper databases show citations for “chicken salad sandwich” in the 1890s and “egg salad sandwich” in the 1900s.
 
       
Wikipedia: Chicken or the egg
The chicken or the egg causality dilemma is commonly stated as “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. “Chicken-and-egg” is a metaphoric adjective describing situations where it is not clear which of two events should be considered the cause and which should be considered the effect, or to express a scenario of infinite regress. Plutarch posed the question as a philosophical matter in his essay “The Symposiacs”, written in the 1st century CE.
   
May 1975, Ladies’ Home Journal (New York, NY), pg. 68, col. 2 cartoon:
“Which came first, the chicken salad or the egg salad sandwich?”
       
Google Books
October 1981, Boys’ Life, “Think & Grin,” pg. 81, col. 3:
Then there was the philosopher who went into a restaurant and ordered an egg salad sandwich and a chicken salad sandwich. He wanted to find out which one came first. — Jay Bryan, Springfield, Mo.
 
29 October 1985, The Morning News (Wilmington, DE), “Knicks learn that one ace doesn’t make a winning hand” by Shelby Strother (The Detroit News), pg. C3, col. 1:
DETROIT—Two friends went into a restaurant and sat at different tables. One told the waitress he wanted a chicken salad sandwich. The other ordered an egg salad sandwich. And they waited…to see which came first.
       
Google Groups: rec.humor
WANTED: Intellectual Humor
T. E. Wemlinger
12/27/94
(...)
Then there was the philosopher who went into the diner and ordered a chicken-salad sandwich and an egg-salad sandwich—to see which came first.
 
6 January 2004, Herald Sun (Melbourne, Victoria), “Watch This Space” by Mike Edmonds, Luke Dennehy & Carla Danaher, pg. 21:
What came first? The chicken-salad sandwich or the egg-salad sandwich?
 
Twitter
mana
@manatronic
Replying to @glitchritual
@glitchritual the chicken salad sandwich you can find dates back to the 1800s in recipe books. the egg salad sandwich is in the early 1900s.
12:35 PM - 5 Jan 2011
     
Reddit—Shitty Ask Science
Which came first, the chicken salad sandwich, or the egg salad sandwich? (self.shittyaskscience)
submitted August 10, 2014 by [deleted]
 
Twitter
Neil deGrasse Tyson
@neiltyson
Damn. One mystery solved & another rears its head: Which came first, the chicken salad sandwich or the egg salad sandwich?
10:55 AM - 20 Aug 2014
     
Twitter
Steve Law
@Evetswal
Which came first?  The chicken salad or the egg salad? #mysteriesoftheuniverse
12:46 PM - 27 Jan 2018
 
Quora
Which came first, the chicken salad sandwich or the egg salad sandwich?
Steve Baker, Blogger at LetsRunWithIt.com (2013-present)
Updated Apr 29, 2018
It’s believed that the egg salad sandwich was invented in France in 1762 - it couldn’t have been much before that because mayonnaise was only invented in 1756.
 
Well, we know that the first modern-style chicken salad sandwich was served by Town Meats in Wakefield, Rhode Island, in 1863.
(...)
So it seems likely that the egg came before the chicken.