not have a (snowball's) chance in hell

not have a (snowball's) chance in hell

To be completely impossible or incredibly unlikely; to have no chance whatsoever. Often followed by "of." That party doesn't have a snowball's chance in hell of winning an election in this part of the state. We don't have a chance in hell of catching up to their score.
See also: chance, have, hell, not
Farlex Dictionary of Idioms.

not have a snowball's chance in hell and not a hope in hell

Inf. a very poor chance. (Usually in the negative.) She doesn't have a snowball's chance in hell of getting it done on time. I know I don't have a hope in hell, but I'll try anyway.
See also: and, chance, have, hell, hope, not
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.

not have a ˌsnowball’s chance in ˈhell (of doing something)

(informal) have no chance at all of doing something: Look at this traffic! I’m afraid we haven’t got a snowball’s chance in hell of getting to the airport in time. OPPOSITE: a sporting chance
This idiom refers to the belief that hell is a place of fire.
See also: chance, have, hell, not
Farlex Partner Idioms Dictionary
See also:
  • not have a snowball's chance in hell
  • not have a snowball's chance in hell and not a hope in hell
  • a snowball's chance in hell
  • snowball
  • snowball’s chance in hell
  • snowball's chance in hell, a
  • on the (off) chance
  • on the chance
  • one chance in a million
  • on the off chance