The limited edition balls feature the official colours and badge from each of the 72 Football League member clubs from the 2015/16 season.
The balls are of the highest quality available, are FIFA Approved, and are the same as the balls the professionals use in training and during Football League games.
Sky Bet’s Head of Sponsorship David Tweed said: “It’s our mission to make things better this season and what better way to do this than to provide an upgrade to the tired footballs being used in kickabouts all over the country?
“These Mitre balls really are top of the range and have the same colours and badges as those used at each of the clubs in the Football League.
“This really is a one-off opportunity to get your hands on a fantastic piece of kit, worth over £100.
“The only question if you win is whether you play with it or try to keep it in pristine condition.”
To enter, fans must visit https://www.skybet.com/cms/making-kickabouts-better.shtm and enter their details.
All entrants must be over 18.