fighting chance

noun
a possibility of success following a struggle.

Origin:
1885–90

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Based on the Random House Dictionary, © Random House, Inc. 2014.
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Collins
World English Dictionary
fighting chance
 
n
a slight chance of success dependent on a struggle

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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American Heritage
Idioms & Phrases

fighting chance

A possibility of winning, but only with a struggle. For example, It's going to be hard to beat that record, but I think he has a fighting chance. [Late 1800s]

The American Heritage® Dictionary of Idioms by Christine Ammer.
Copyright © 1997. Published by Houghton Mifflin.
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Example sentences
To stand a fighting chance, the ideas in your project must be both good and
  well positioned relative to other grant proposals.
The fairness in that is that if you are given enough information and resources,
  you have a fighting chance.
Then, in theory, the government will establish its authority and will have a
  fighting chance.
He is an insurgent whenever there is a fighting chance it will do him any good.
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