A real but limited possibility of success in a difficult situation.
Using the reference
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A fighting chance is a genuine, though not comfortable, possibility of success.
This phrase sits between hope and realism. It says the odds are not easy, but the situation is not hopeless either. The speaker thinks effort, skill, or persistence could still matter.
People use this expression when describing underdogs, risky plans, difficult negotiations, medical recovery, or any situation where success is possible but far from guaranteed.
The wording likely owes part of its force to boxing and other contest language, where staying competitive matters even when the odds are long.