Can I take a Chinese class although I'm fluent?

Depends on what level of course. The East Asian language department does offer various levels of Chinese courses for heritage speakers as well as high level courses that should be suitable for those with good fluency and literacy. Not all native or heritage speakers have full fluency and literacy (note that native English speakers in the US are expected to take English courses in high school and college).

The OP should take the placement test to find out which courses are appropriate for him/her.