Yes. Chlamydia may be a silent infection for years. Even though it it not causing any overt symptoms, it may be causing inflammation of the the cervix, the uterus, and the tubes. Over time this can result in damage to the tubes that may affect fertility. It is important to have a PCR test for chlamydia if you have had sex without condoms with a partner who could be infected.
Reinfection. Signs of chlamydia range from asymptomatic (therefore "dormant") to pain or drip/discharge. Incubation is 1-3 weeks. Untreated, chlamydia can lead to sterility in women & chronic prostatitis in men. Reinfection is very common in young adult age group. Screening is the best preventive other than barrier protection. See http://emedicine.Medscape.Com/article/214823-overview#a0104.