“Fat chance” actually means slim or no chance. “Fat chance” shouldn’t be confused with “fat chants,” but there are jokes.
   
“My wife seems to think that reciting a mantra is gonna help her lose the weight she gained over Christmas. Fat chants” was posted on Twitter by GlennyRodge on December 30, 2011. “Weight loss mantra? Fat chants!” was posted on the website Pun of the Day on July 6, 2012.
   
     
Twitter 
GlennyRodge
@GlennyRodge
My wife seems to think that reciting a mantra is gonna help her lose the weight she gained over Christmas. Fat chants.
2:41 AM - 30 Dec 2011
   
Twitter
The Poke
@ThePoke
My wife seems to think that reciting a mantra is gonna help her lose the weight she gained over Christmas. Fat chants. (RT @GlennyRodge)
3:04 AM - 30 Dec 2011
 
Pun of the Day (July 6, 2012)
Weight loss mantra? Fat chants!
Category - Health and Medicine
Submitted by - Irish Limbo - Auckland
 
Twitter
Crack Me Up
@haha_2funny
Pun of the Day: July 6, 2012 - Weight loss mantra? Fat…: Weight loss mantra? Fat chants!... http://bit.ly/NGn1xW  http://punoftheday.com
3:03 AM - 6 Jul 2012
 
Twitter
Nelson Mendez
@Bennyties
July 6, 2012 - Weight loss mantra? Fat… - Weight loss mantra? Fat chants![Click to Vote!] http://ow.ly/1l9ItI
8:48 PM - 6 Jul 2012
     
Twitter
PUNS
@omgthatspunny
Weight loss mantra? Fat chants!
2:46 PM - 1 Aug 2013
 
24 August 2013, Edmonton (Alberta) Journal, “Cryptograms” by Myles Mellor, pg. G12, col. 3:
Last Week’s Cryptograms
(...)
2. I was looking for a dieting mantra. My doctor told me it was unlikely I would get one and ended with: “fat chants.”
 
Twitter
Michael Bullock
@MBullock92
Apparently you can lose weight by repeating a slimming mantra over and over… Fat Chants!
#1PUN
8:06 AM - 12 Sep 2013
     
Google Books 
Tales From Here There and Everywhere:
50 Short Stories
By Don Conway  
PublishNation LLC (PublishNation.net)
2016
Pg. 30:
Next, someone called out “Dieting.”
 
My reply was, “Weight loss mantra — fat chants.”
 
Groans from the crowd told me I was on the right track.
 
27 December 2017, Topeka (KS) Capital Journal, “An inexhaustible supply of puns” by Mike Hall, pg. 101:
Do you have weight loss mantras? Fat chants!
 
Twitter
Jayne Pattullo
@LadyPattullo
Weight loss mantra
Fat chants ☺️
4:53 PM - 28 Jan 2019