Does the metronidazole antibiotic cure BV and chlamydia?

Not both. Metronidazole will often cure BV (bacterial vaginosis). It is ineffective against chlamydia. For this you will need a different antibiotic, such as azithromycin, doxycycline, eryhromycin, or uncommonly Levofloxacin and ofloxacin. See your clinician for an appropriate prescription.