Can a chinese citizen living in China sue a US based pharmacutical
company for personal injuries sustained from taking a prescription
drug manufactured by the US company?  If so, could they sue in the US?
 Are there any laws or issues that might prevent the chinese citizen
from bringing his case in the US?

The company most likely can be sued in the United States.  The
specifics, however, will depend on what state you sue in.  You'll have
to sue in the headquarters state, or in some cases, you can also sue
in the state of manufacture.

The complication, however, will involve the "choice of law."  As the
injury occurred in China, some states' law will require that the
state/federal courts there use Chinese law (which would make for some
interesting judgments given that the American judges ordinarily can't
read Chinese).  Other states will impose local law.

In some rare cases, the case could be dismissed for "forum non
conviens", essentially forcing you to bring suit only in your own
country, but more often than not (depends on the state), the courts
won't block you.

I would talk to an American lawyer in the state of the company's
headquarters, plants, or primary place of business to get a better
answer.

--Joey

Do they have a subsidiary in China?

The US company has offices in China.