You could say either "China's chemical industry" (because you're talking about the chemical industry that belongs to China) or "the Chinese chemical industry" (I would prefer this option as it sounds more formal). The definite article "the" is required because there is only one Chinese chemical industry. Similarly, I would talk about "the Brazilian beef industry" or "the Indian tea industry". However, if you were talking about only one company in the industry, you would say "a Chinese chemical company". This is because there are many companies and you'd only be talking about one. I hope that makes sense.

China's is formally used in official papers in the government under this context to avoid ambiguity. China is where Chinese originated but Chinese do not necessarily live in China for the moment... so there you can see the difference.