A popular joke has a man visit a psychiatrist, saying, “Doctor, my son thinks he’s a chicken.” The psychiatrist suggests that the boy be sent to an institution. “We’d like to do that,” says the man, “but we need the eggs.”
New York City-born actor, singer and comedian Eddie Cantor (1892-1964) claimed in 1950 that he had originated the joke a decade previously. Bronx-born film director, writer and actor Woody Allen included the joke in his New York film classic, Annie Hall (1977).
30 November 1950, The Morning Herald (Uniontown, PA), “It Happened Last Night” by Earl Wilson, pg. 4, col. 2:
TODAY’S BEST OLD LAUGH: Eddie Cantor says he originated psychiatrist gags a decade ago, this way: “Doctor, my son thinks he’s a chicken"..."Bring him in and I’ll look at him"..."I would, but we need the eggs.”
31 May 1951, Greensboro (NC) Record, “Turpentine Drippings,” pg. C-8, cols. 1-2:
A man paid a call on a psychiatrist, and told the doctor he would for him to come out and talk to his brother.
The psychiatrist asked the man for a description of his brother’s case.
“He thinks he’s a chicken. Flaps his arm and cackles around the house all day long,” the man explained.
The psychiatrist studied a moment, and then said, “Hmmmmm. Well, I’m afraid there isn’t much I would be able to do for your brother. Have you thought about having him sent to some kind of institution?”
The visitor looked the doctor straight in the eye and replied, “Yes. We’ve thought about that, but to tell you the truth, doctor, we need the eggs.” (Goldsboro News-Argus)
26 September 1951, The Oregonian (Portland, OR), “Behind the Mike” by William Moyes, sec. 2, pg. 2, col. 1:
HERE’S a TV silly: Guy with string of red life savers hanging from left ear and green string from right ear drops in to see psychologist about his brother. Doc asks what’s wrong with him. Guy says “He thinks he’s a chicken.” Doc asks why don’t you put him away. “We thought of that,” replies the guy, “but we need the eggs.”
17 February 1952, The Idaho Sunday Statesman (Boise, ID), pg. 11, col. 1 ad:
DICK LOGSDON’S SMILE SECTION:
Moron: “My brother thinks he’s a chicken.”
Psychiatrist: “Why don’t you tell him different?”
Moron: ‘I would, but we need the eggs.”
(Logsdon Motor Company.—ed.)
IMDb (The Internet Movie Database)
Annie Hall (1977)
Alvy Singer: [narrating] After that it got pretty late, and we both had to go, but it was great seeing Annie again. I… I realized what a terrific person she was, and… and how much fun it was just knowing her; and I… I, I thought of that old joke, y’know, the, this… this guy goes to a psychiatrist and says, “Doc, uh, my brother’s crazy; he thinks he’s a chicken.” And, uh, the doctor says, “Well, why don’t you turn him in?” The guy says, “I would, but I need the eggs.” Well, I guess that’s pretty much now how I feel about relationships; y’know, they’re totally irrational, and crazy, and absurd, and… but, uh, I guess we keep goin’ through it because, uh, most of us… need the eggs.
But We Need the Eggs: The Magic of Woody Allen
St. Martin’s Press, Jul 1, 1983 - 192 pages
OCLC WorldCat record
I would, but I need the eggs : why neither exit nor voice substantially limits big city corruption
Author: David Schleicher
Publisher: [Arlington, Va.] : George Mason University School of Law, 
Series: George Mason University law and economics research paper series, 11-11.
Edition/Format: Print book : State or province government publication : English