From Longman Dictionary of Contemporary Englishhave a fighting chancehave a fighting chanceCHANCE/OPPORTUNITYto have a chance to do something or achieve something if you try very hard Lewis has a fighting chance to win the gold medal. → fight
Examples from the Corpus
have a fighting chance• All children must have a fighting chance at a good education.• Central defender Tony Mowbray believes his former team have a fighting chance at Old Trafford.• And that has encouraged the Geordies to believe they still have a fighting chance of keeping him. 