I am trying to apply for a Chinese tourist visa. I was born abroad in country A but acquired US citizenship at birth through one of my parents. I also had A's passport that was acquired when I was a little kid. (It was later cancelled when I legally "acquired" the US citizenship.) In the application form, do I note in my application that I was a former national for A?
Dealing with hypotheticals makes it difficult to answer... For example, if country "A" is China, then yeah, you have to disclose that. Besides this particular case, the general rule is, if there is a question on the form, you answer it. If there isn't, you don't volunteer any information.
So check the form: is there a question about former citizenships? If yes, say so, if not, you don't even have a space to write down this piece of information anyway.
I just checked and the form (from the Chinese Visa Center in Paris) asks this:
1.6 Current Citizenship vs 1.7 Birth Citizenship if different.
So yeah, you need to give both.
You were a dual citizen: a US citizen at birth and a citizen of the country in which you were born. At some point, you relinquished the latter (as used to be required of born abroad US citizens when they reached the age of 18).
However, that visa application form is not asking about dual nationality: you can correctly respond to question 1.6, nationality, USA, and leave 1.7 blank, unanswered.