The first thing to clarify is what chlamydia test was done. A chlamydia blood test often is done in evaluating couples for possible infertility. If positive, it usually indicates past infection, not current. (Some providers, mostly outside the United States, mistakenly use the test to try to diagnose current infection, often causing confusion due to falsely positive results.) So if that's the test that was done, to be safe, he should have a urine test for current infection--but most likely he is not infected.
If your husband had standard testing of urine or a urethral swab, it still could be a false positive result, although the likelihood of this explanation depends a bit on the particular test that was done. Of course you should have a non-judgmental, sensitive, heart-to-heart discussion with your husband about the possibility he in fact has had other partners. As you already know, chronic carriage for 11 years is an unlikely explanation; such prolonged infection has never been documented (and rarely even suspected) in men. That doesn't prove it can't happen, but it is the least likely of all the potential explanations for your situation.
I hope this helps. Best wishes-- HHH, MD
Even if he has been unfathfull I don't think you should end the relationship with him if everything else is going well? Talk with him. I can tell you from experence that I was 100% faithful for 8 years in my relationship, then I came to the point of wanting to break off this great relationship just so I could go out and screw some new, I decided to cheat and it was the best thing for my relationship! I know it sounds crazy but now I apprciate my relationship more, and it really does mean nothing at all in most situations for the man. Good Luck..