“Chicken, airplane, soldier” is how many swim instructors explain the backstroke to young swimmers. Hands are under the armpits (like a chicken), then arms are spread directly out (like an airplane), and then arms are brought straight down directly to the body (like a soldier standing at attention).
   
“Chicken . . . airplane . . . soldier” was cited in Froggy Learns to Swim (1995).
 
   
Google Books
Froggy Learns to Swim
By Jonathan London
New York, NY: Viking
1995
Pg. ?: 
And she showed Froggy how, saying: “Chicken . . . airplane . . . soldier.”
 
13 May 1998, Hutchinson (KS) News, “High school seniors teach kids to swim” by Kelly McGuire, pg. A2, cols. 5-6:
Their group instructor, Trisha Becher, taught them the arm movements by remembering three simple words—chicken, airplane, soldier.
 
Chicken means to tuck your hand under your arms, like a chicken would look flapping its wings. Airplane means arms straight out from your sides. And soldier means arms flat against your sides as if you were standing at attention.
 
Put the three together in a fluid motion, throw in a power kick and you’re doing the backstroke.
 
Google News Archive
13 August 2001, The Free Lance-Star (Fredericksburg, VA), “SWIM: Senior gets past fear, learns to swim,” pg. D2, col. 4:
Then in what Mary describes as the chicken-airplane-soldier stroke, Bernice draws her hands up under her armpits, thrusts her arms straight out, then presses them down to her thighs.
 
YouTube
Chicken, airplane, soldier.
Leslie Courchesne
Uploaded on Aug 12, 2009
Tyr’s swimming lesson at Black Mountain Ranch, WA. August, 2009.
 
YouTube
Ava swimming to Elvis, “Chicken, Airplane, Soldier”.
SydFarr
Uploaded on Nov 14, 2009
swimming
 
Twitter
Clarisa Gerlach
‏@clarisagerlach
My lil one doing the backstroke. Say it with me: chicken, airplane, soldier. http://tweetphoto.com/6738800
8:23 AM - 19 Dec 2009
 
YouTube
CHICKEN! AIRPLANE! SOLDIER!
jasper is your friend
Published on Jul 14, 2012
Swim lessons, day two.
 
Twitter
SwimInstructorProbs
‏@swiminstructorp
If I have to tell one more kid to hold the glide after chicken airplane soldier one more time I swear…
5:26 PM - 14 Oct 2013
 
Google Books
I’d Rather Be Swimming!
By Joan and Peter Leonard
Bloomington, IN: Archway Publishing
2015
Pg. 23:
SNOW ANGEL
(ELEMENTARY BACKSTROKE WITH WHIP KICK)
1. Be an Upside-Down Shark.
2. Armstroke: “Chicken,” bend your arms and bring your hands up along your side until they are to your armpits. “Airplane,” stretch your arms straight out. “Soldier,” sweep your arms down to your sides, feeling the water with straight arms and hands.