Hi, amateur (and minor degree holder) of Chinese history, language and culture here. This is somewhat dependent on the historical period, but there is evidence of chattel slavery (along with convict slavery) used for megastructures like the Great Wall and irrigation/land reclamation projects in the flood plains during the Qin and Han. There is also evidence that the caste systems during and preceding the Han supported inherited slave-status, i.e. you were a slave if your mother was one. This shows up in Confucian works occasionally. The popularity of slavery seems to have waxed and waned throughout China's dynastic eras. One of my Chinese professors explained the Chinese word 人民 renmin as proof of social stratification and evidence of feudal slavery. Not sure how right he was on that, but interesting idea.

IMO traditional bondage and commodification of women in China counts as slavery, and that's seen throughout its entire history. Not chattel slavery but slavery nonetheless.

Expansionistic dynasties surely would have taken war slaves, and there seems to be evidence of this in various complied histories like the Tangshi. Of course, you have the Yuan dynasty that enslaved many peoples both endemic and foreign to China, and the rendering of the native Chinese to second class citizens. This occurs during Qing (they were invaders as well), but you see a decline and eventually abolition of slavery post 1909. This did not really end indentured servitude or convict labor systems that were then adapted by the CCP's Laogai system (Chinese analog of the Soviet gulag).

I don't know if one has ever found any evidence for the chattel slavery similar to the American South's systems, but I'm guessing it's probably still possible, although many of the conditions that made the American system monolithic (colonialism, capitalism, industrialist, etc.) may not have been so at any point in Chinese history.

I have not read many scholarly works on slavery in China, but the evidence for multiple systems of slavery do seem to exist throughout its history, from imperial correspondences to pieces of art. It would be worth research, and would make a good history grad thesis.