Can you get a false positive on a urine test for chlamydia?

Very unlikely. Urine test for chlamydia has comparable sensitivity and specificity as cervical or urethral specimens which are high if NAAT was use as a test (Nucleic acid amplification tests (NAATs).
Possible. False positives are always possible, although unlikely. Without know the actually type of test used, it is not possible to estimate the false positive rate. That being said, a positive result should be taken seriously and assumed to be correct, and treatment for you and your partners should be undertaken immediately.