The first Chinese born Nobel prize winnner is a fellow named Walter Houser Brattain, who co-invented the transistor. Transistor is a big invention even by Nobel prize standards, and he won the prize on 1956. If you've noticed that his name does not sound like Chinese, he is not, and he worked at the famous Bell Labs with Shockley and Bardeen.
The next question is who was the first Nobel Prize winner of Chinese ethnicity. That would be Yang Chen Ning and Tsung-Dao Lee, who shared the Prize a year later, on 1957. Yang went to the US with a scholarship from Boxer Indemnity (庚子賠款), as are many other famous Chinese scientists/people of the time. It is definitely one of the most successful scholarship program in history, with all 30 recipients having and deserving wikipedia pages . Granted, they did their work in the United States, not China, and they are American citizens. Chinese Americans will then go on to win 6 more Nobel Prizes in the Sciences. They are Samuel C. C. Ting (丁肇中), Yuan T. Lee (李遠哲), Daniel C. Tsui (崔琦), Steven Chu (朱棣文), Roger Y. Tsien (錢永健) and Charles K. Kao (高錕). Though this is really not a very Chinese crowd, with half of them born in the US, and one even became the US Secretary of Energy under the Obama administration.
The next question is are there winners who are more Chinese. Well, there is a fellow named Tenzin Gyatso, aka the 14th Dalai Lama, who won a rather undeserved peace prize on 1989 like Obama and EU. It is still a Nobel prize, though the Party would love him to be Chinese, he does not consider himself Chinese.
So is there any Nobel prize winner who considers himself Chinese? There is Liu Xiaobo, who admits himself to be Chinese, was born in China, and did his Nobel Prize worthy work in China. But then, the Party does not acknowledge his existence, and he did not even get to attend the ceremony and he is probably in prison at best. In any event, the Party would love it for him to leave China and become a US citizen or something.
Finally, there is Mo Yan (莫言) who won the Literature Prize in 2012. Mo was born in China, did his work in China, and is accepted by the Party and the people. Thus a definitive yes is finally the answer to the question “has a Chinese person win the Nobel prize” 56 years after Brattain. The guy who is writing a thesis on “On the separation between China and Nobel prize” can finally stop, or add the qualifier Science in front of Nobel Prize.