In the US atleast, the term "Chinaman" is considered offensive towards the Chinese people. In early US history during the very beginning of Chinese imigration to the US, they were often called this and at the time was not considered offensive, but it has since been defined as an offensive term by many organizations and is defined so. Chinese can be applied singularly or pluraly. He is Chinese. They are Chinese. We are Chinese. It is the accepted term used to reference a person of Chinese nationality or heritage. Outside the US it may be different, I'm not sure. ^^

My answer to this question is basically to confirm Mytch's excellent answer. The term Chinaman is rarely if ever used anymore in the US. It is considered offensive, certainly when compared merely to the adjective Chinese, which may refer to people, food, products, etc.. Exactly why it is considered derogatory is perhaps a better and more fascinating question. Certainly 中國人 isn't considered offensive in the Chinese language, nor 英國人, 法國人, 等. But in English, it's not good. It is almost as if you are singularly associating the person with a specific all-defining trait, and moreover, using incorrect grammar to do so (China as an adjective rather than Chinese).

the offensive chinaman you mean is 支那人吧，what the japanese used to call the china people. i will never called myself chinaman since i am not from china. i am a chinese from malaysia.

Chinese would refer to the people as a whole. Chinaman is only speaking about one person, who would be male.