snowball's chance in hell, a - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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]