When did the Chinese begin making silk?

Silk cloth was first made in China about 5000 years ago. However, silk thread existed in China long before someone decided to make cloth from it.

The silk used for weaving cloth comes from the cocoons of the bombycidae type of moth. The moth lays eggs which hatch into larvae (caterpillars) which become pupae. The pupa wraps itself in a cocoon that it makes from the silk thread it extrudes from glands in its mouth.

Pupae had been making silk thread long before humans discovered what their cocoons were made of. So it is quite possible it was hundreds of millions of years ago that the very first insects invented silk in China.