a snowball's chance in hell

1. Something that has no likelihood of happening or succeeding: “Your proposal is too radical — it has a snowball's chance in hell of being approved.”

Idioms and Phrases

No chance at all, as in He hasn't a snowball's chance in hell of getting there in two hours . This idiom, nearly always used negatively, alludes to the traditional view of hell as extremely hot, causing snow to melt at once. [Late 1800s]