As for studying China in general, there are many universities which allow you to major in this, although it’s usually found under a larger subject such as “Asian Studies” or similar. Start with the following, all of which I believe offer Asian Studies, which you can focus on China:

– New York University

– UMass Amherst

– Emory

– Vassar

– Holy Cross

– SUNY Buffalo

– Pomona College

– St. Lawrence

– Cornell

– Columbia

– Smith College

And specifically to major in “Chinese studies”, I see that exists at:

– U Hawaii Manoa

– University California San Diego

And those are just a few. As you can see, it’s a major that you can find at all types of universities.