A fighting chance
Definition 1 of 1
Pro Tip 1/3Positive Connotation
Implies hope or optimism in challenging situations, suggesting there's still a chance to win or succeed. 
The team lost the first two matches, but they still have a fighting chance to take the championship.
Pro Tip 2/3Not a Guarantee
Doesn't promise success, but indicates the possibility is there if effort is made. 
If she prepares well for her interview, she's got a fighting chance of landing the job.
Pro Tip 3/3Colloquial Usage
Common in everyday English, especially in informal speech and writing. 
With some hard work, you've got a fighting chance at improving your English.