A fighting chance - Idioms by The Free Dictionary
a fighting chance
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A small possibility to succeed or overcome a situation. David wanted to give his marriage a fighting chance so he agreed to go to counseling with his wife. If I'm going to have a fighting chance to pass this test, I'm going to have to study all night.
a ˌfighting ˈchance a slight but real chance of succeeding, avoiding something, etc: With five minutes of the game left, our team still has a fighting chance of winning. ♢ Things don’t look very hopeful for John Brown in the presidential elections, but he’s still in with a fighting chance.