1
general::
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]
American Heritage Idioms
2
general::
Phrase(s): a fighting chance
a good possibility of success, especially if every effort is made. • They have at least a fighting chance of winning the race. • The patient could die, but he has a fighting chance since the operation.
McGrawhill's American Idioms And Phrasal Verbs