People is already plural. Peoples would mean there were several groups of different people. So, you should say a friend of the Chinese people.

Hi Joanna, This is a tricky one! This construction is referred to as the "double genitive", "double possessive", or "oblique genitive". It is an old construction (used by Shakespeare, for instance). The important point is that it is used to refer to individuals and this is why it can't refer to the people of China. If you search online for the phrases in quotation marks, you should find more information. Good question, Joanna, and I hope that helps! Gus