I am a US citizen in Ukraine & am applying for TEFL jobs in China. What visa requirements are there?

Foreigners who come to China to take up employment as experts, scholars, teachers, managerial personnel and as personnel working in related state or local organizations should provide:
1. Permit for Foreign Experts Working in China issued by the State Bureau of Foreign Experts (original); and
2. An Invitation Letter of Duly Authorized Unit issued by an authorized unit in China (original).

Your employer has to send the two documents to you, then you can use them to apply for China work visa, you can also do medical check up in an authorized hospital in Ukraine