Applicants between the ages of 14 and 70 need to have their fingerprints taken when applying for the Chinese visa, so they must submit their application in person at the Visa Center. Other applicants may may entrust someone else to do it for you (no need to provide a power of attorney) providing that you have prepared all the documents required and signed the application form.
However, citizen of other countries are required by the Chinese Embassy and Consulate-General to submit the applications person to the Visa Centre.