Translation:Today at noon I have a Chinese exam.
The translation provided is actually wrong. The correct translation for this sentence should be "Today at noon I have an exam in Chinese" and not a "Chinese exam". Although it is grammatically correct, the semantics is wrong. The adjective "Chinese" implies ORIGIN as in Chinese food, language, tradition, etc., ...but "an exam in Chinese".
I agree for an additional reason. The translation suffers from multiple ambiguities. What is a Chinese exam? " … I have a Chinese exam" could apply to an examination on history that is written in Chinese, or one that is written in any language but produced in China -- as well as being a test of one's proficiency in the Chinese language which is what the Italian version probably means. Following the Italian literally, I wrote "Today at noon I have a test of Chinese", but it was marked wrong by DL. I reported it.
I think you're splitting hairs. An exam in Chinese and a Chinese exam would be taken by most students of Chinese to mean the exact same thing. You hear students all the time say I have a French test today or an exam in German. They're all saying the same thing essentially. To assert otherwise is nonsense.
Richard...Without specifying what the "same issue" actually is, given the number of comments pro and con above yours, it's hard to respond. My feeling about the question of whether it should be: Chinese exam or exam in Chinese is below. In brief, to me both phrases are synonymous and should be acceptable.