Chinese workers were sent into tunnels and construction sites to ignite dynamite, potentially with disastrous consequences.
They were also lowered over cliffs by rope and boatswain's chairs to set dynamite to clear mountain and other obstructions to make way for the railroad construction. In this work, if they were not lifted back up before the blast, serious injury or death would result.
Therefore the phrase "A Chinaman's Chance" may have been coined in this context.
“You haven’t got a Chinaman’s chance,” also refers to the practice of white railway workers preparing a dynamite bundle, cutting the fuse short and giving it to a Chinese worker to take into a tunnel.
When he lit the fuse, he had only seconds to run out ahead of the blast. Wagers were placed on his chance of making it. Most did not.