Can chlamydia go away on its own without treatment?

Yes it can: Chlamydia almost always is cleared by the immune system, without antibiotics. It takes a few months or even a year or two. In the meantime it can cause terrible damage to the reproductive system. If one partner is infected and the other has a negative test, it is possible the test missed the infection; the tests are good but not perfect. The partner with the negative test still needs treatment.