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.
di BrianSnat 15 luglio 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.
di Scott Delhommer 27 aprile 2008