"Chinaman's Chance" appeared in the Sept. 1935 issue of Black Mask. As far as I know, it is one of only five Paul Cain stories that have never been reprinted. Three of the others were also in Black Mask, while the fourth, "555" (mentioned in yesterday's review of Fast One), was in the December 14, 1935 issue of Detective Fiction Weekly.
I have both "Chinaman's Chance" and "555" and would be pleased to share them with readers of the Almanack. For one reason or another I won't be posting the stories on the blog, but if you'd like copies of the scans via email, just shoot me a message at firstname.lastname@example.org
(click to enlarge)