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.
Words nearby not have an earthly chance
not give a damn,
not give someone the time of day,
not half bad,
not have a bean,
not have a clue,
not have an earthly chance,
not have anything on,
not have it,
not have one's heart in it,
not have the heart to,
not having any