Yes, it should clear up chlamydia. Both Zithromax (which is azythromycin) and Vibramycin (doxycycline) are the antibiotics commonly used to treat and cure chlamydia.
Zithromax may help treat any infections that you may have that the chlamydia has caused, but it will not clear up the actual sexually transmitted disease. There are other medications to take that treat that.