It's a boxing term. It means that though you may be outclassed by your opponent, if you land a good punch, you can win.
Bob was down in the polls, but if he did well in the debate, he'd have puncher's chance of winning the election.
by BrianSnat July 15, 2015
term used in boxing to describe something that has a slight chance of happening
I thought i had a puncher's chance of going out with her even though she's the hottest girl in school.
by Scott Delhommer April 27, 2008