Chinaman's Chance Meaning

(idiomatic, offensive) No chance; zero possibility; a high or almost certain risk of death or failure.

Example: 2005, Richard Corliss, "Anna May Wong Did It Right," Time, 29 Jan.,
  The Chinese, who in the mid-19th century had come to America by the tens of thousands and helped build the transcontinental railway, were on the receiving end of much prejudicial legislation. . . . In the slang wisdom of the day, sojourners from the Middle Kingdom "didn't stand a Chinaman's chance."