Historically, Chinaman was a neutral compound word, similar to Irishman or Englishman , but it began to take on negative connotations in the 19th century, when many Chinese immigrants went to work in the American West. The expression a Chinaman's chance originally made reference to these Chinese laborers, though the exact origin of the phrase is disputed.
Also, ghost of a chance. An extremely slim chance, a hopeless undertaking. Both versions are most often put negatively, as in He hasn't a Chinaman's chance of finishing the work in time, or They haven't a ghost of a chance to get as far as the playoffs. The first term, now considered offensive, dates from the late 1800s when many Chinese immigrants came to work in California and were resented because they worked for lower wages. Its precise allusion is unclear. The variant, which relies on the meaning of ghost as an insubstantial shadow, dates from the mid-1800s. Also see the synonyms fat chance; not an earthly chance.