I am a german passport holder and I need to apply for a Business Visa for China.

But how about your status there? as I know, temporary visitors can not apply if they do not have residence permit or valid long-term visa.

Anyway, if you have above document and reside within consular jurisdiction of the consulate in Chiangmai, you can submit your application to the consulate. Generally, the express service takes about 2-3 working days.