“I’m so hungry I could eat a horse and chase the rider”

“I’m so hungry I could eat a horse” is a saying from the 1700s and 1800s, when horses were used for transportation (and eating the horse would be a last resort). “I’m so hungry I could eat a horse and chase its/the rider” means that the speaker is even more hungry.
 
“He can eat a horse and chase the rider up a tree any day” was printed in an 1866 story. “I’m hungry enough to eat a horse and chase the rider” was printed in the New York (NY) Times in 1893. The expression was only infrequently used, but it became popular in Australia in the second half of the 20th century—long after horses were used as transportation.
 
     
Wiktionary: I could eat a horse
Phrase
I could eat a horse
1. (idiomatic, hyperbolic) I am very hungry; short form of “I’m so hungry, I could eat a horse.”
 
Chronicling America
5 July 1866, Wilmington (NC) Journal, “The Dog Gondest Dog!” by Brick Pomeroy, pg. 2, col. 6:
He can eat a horse and chase the rider up a tree any day, and were it not for his peculiarities, would be a fine dog.
 
Google Books
Nonsense, Or Hits and Criticisms on the Follies of the Day
By “Brick” Pomeroy
New York, NY: G. W. Carleton & Company, Publishers
1869
Pg. 93:
He can eat a horse and chase the rider up a tree any day, and were it not for his peculiarities, would be a fine dog.
     
28 September 1876, Forest and Stream, “On the Wilderness Trail,” pg. 114, col. 2:
... he pulled up in front of the Feuton House and let out three men hungry enough to “eat a horse and chase the rider.”
 
9 July 1893, New York (NY) Times, pg. 4, col. 7:
Jess ( in restaurant)—“I’m hungry enough to eat a horse and chase the rider.”
Bess—What are you going to order?
Jess—Waiter, bring me three cream puffs and a cup of cocoa.
 
Chronicling America
3 August 1893, Iron County Register (Tronton, MO), “Pith and Point,” pg. 3, col. 7:
Jess ( in restaurant)—“I’m hungry enough to eat a horse and chase the rider.”
 
6 October 1938, Northwest Arkansas Times (Fayetteville, AR)  “Plain Tales from the Ozarks” by Fred Starr, pg. 9, col. 2:
The other countered by saying he was so starved he could eat a horse and chase the rider.
   
Google Books
Body, Boots, & Britches: Folktales, Ballads, and Speech from Country New York

By Harold William Thompson
Philadelphia, PA: Lippincott
1939
Pg. 499 (Proverbs):
I could eat a horse and chase its rider.
 
Google Books
The Lake Guns of Seneca and Cayuga, and Eight Other Plays of Upstate New York
By Alexander Magnus Drummond, Robert Edward Gard
Ithaca, NY: Cornell University Press
1942
Pg. 140:
I could eat a horse and chase its rider!
 
Google Books
Lily on the Dustbin:
Slang of Australian Women and Families
By Nancy Keesing
Ringwood, Australia; New York, NY: Penguin Books
1982
Pg. 118:
Threatened with such unappetising dishes it is an advantage to be so hungry that ‘I could eat a hollow log full of green ants’ (a distinctively northern New South Wales or Queensland expression), or ‘I could eat a horse and chase the rider.
 
Google Books
The Lingo Dictionary of Favourite Australian Words and Phrases
By John Miller
Wollombi, New South Wales: Exisle Publishing Limited
2009
Pg. 63:
Other sayings are could eat a horse and chase the rider and could eat a horse if you took its shoes off.
 
Twitter
Mary-Denise Smith
@CrumbsnRubble
Replying to @nortonofmorton @EnglishUtopia
Ha! My Mom used to say “So hungry I could eat a horse and chase the rider”!
6:42 AM - 14 Nov 2016