snowball's chance in hell, a
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]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.