not have an earthly chance
American Heritage Dictionary of Idioms:
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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.
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American Heritage Dictionary of Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Company. All rights reserved.
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