Here are some examples:
* The Chinese language is tonal.
* He is studying Chinese history.
* I love Chinese food.
However, you wouldn't capitalize "Chinese" if it refers to something made in China:
* She bought a Chinese vase.
* He wore a Chinese silk shirt.
The key is to think about whether "Chinese" is acting as an adjective describing something specific or as a noun referring to a group of people or a language.