Not a chance means no way, definitely not. It's a flat no with two uses. A prediction: 'Will the whole team fit in that car?' 'Not a chance.' And a refusal: 'Would you sell your grandmother's notebook?' 'Not a chance.' It's conversational and decisive. If you continue, use of plus -ing: not a chance of finishing today.
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Not a chance!; not a chance of + -ing; not a chance that + clause
- Will the whole team fit in that small car? — Not a chance.
- There is not a chance of finishing the mural before the paint arrives.
- Would you sell the notebook your grandmother gave you? — Not a chance.
What changed
First versionThere is not a chance of finish the mural today.
RevisionThere is not a chance of finishing the mural today.
A chance to win is correct, so the plain verb feels natural after chance. But after of, the verb takes -ing: not a chance of finishing. With finish changed to finishing, the sentence works.
No chance means the same and sounds just as casual: 'Can you lend me a hundred pounds?' 'No chance.' Out of the question is stricter and fits an official refusal: Late submissions are out of the question. Not a chance is more emotional and emphatic.
Your turn
Can we walk across town in two minutes? — Not ___ chance.
Show the answer
a — The fixed reply is Not a chance, with the article a. Nobody says Not any chance: there's only Not a chance or No chance.
A friend suggests running a marathon this weekend with no training at all. Refuse in one sentence with not a chance.
Run a marathon this weekend? Not a chance — I haven't trained at all.
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