Is it possible for a woman be tested and have chlamydia but her male partner does not?

Nothing is....: Impossible. But a guy can say that he had a test and it was negative even if he has not had a test at all. It happens . If you do have chlamydia, he needs to see someone, get tested and be treated too. Then after treatment, you both should have repeat tests in 6 weeks or so to be sure that it was eradicated. All partners of both of you should be seen and treated. Good luck!