This is how the US naturalization oath begins: "I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty, of whom or which I have heretofore been a subject or citizen; ..."

It is true that you have to renounce your US citizenship to a Consul for the US to consider you no longer a subject of its (taxation power :-).

If a Chinese American travels to China using Chinese passport instead of a visa issued by the Chinese government he or she would not be able to obtain consular support if he/she runs into legal troubles. If he/she wants a visa from the Chinese government and consular support from the US embassy then he/she can't pretend to be a Chinese citizen any longer.