My girlfriend tested positive for chlamydia but I don't have symptoms. Do I need to be tested?

The technical answer is no, but that’s because you should just receive treatment from her doctor or from the health department anyway. However, if she wasn’t given extra medicine to give to you, the best idea is for you to go see your own doctor for testing and treatment. There are a few other STIs that you should be tested for as well.

As you seem to know, chlamydia is spread through sex. That’s why it’s called a sexually-transmitted infection (or an STI). They used to be called STDs (for sexually-transmitted diseases) but, for the most part, you really don’t spread diseases. You spread infections. 

You stated that you don’t have any symptoms. That’s great! Unfortunately it doesn’t mean that you don’t have the infection. Sometimes STIs sit quietly while they get passed to more and more people. Sometimes STIs do bad stuff to your insides (specifically your reproductive organs) and damage your ability to have children in the future. Whatever the situation, STIs need to be treated. After receiving the medicine, you need to wait a week before you have sex again. Otherwise you might not kill the infection.