Also, not a prayer. No chance at all, as in There's not a hope in hell that we have a winning bid, or If you don't watch the conductor you won't have a prayer of coming in on time. The first term was first recorded in 1923, the second in 1941. Both allude to the chance for heavenly salvation. Also see snowball's chance in hell.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.