not have an earthly chance

Also, stand no earthly chance. Have no chance whatever, as in She doesn't have an earthly chance of getting into medical school, or Bill stands no earthly chance of winning the lottery. The use of no earthly in the sense of “no conceivable” dates from the mid-1700s.

The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.