How long can you be infected with chlamydia before you start getting serious symptoms?

Women may not. The majority of women with chlamydia infection have no symptoms at all. Some women and men experience pain with urination or sex, or abnormal discharge from the genitals. If you have had unprotected sex, or have a new partner, it is a good idea to visit a doctor to be tested for std's. Some women experience problems related to pelvic inflammatory disease and infertility.
A very long time. Chlamydia infection may be inapparent, especially in women. For this reason, the cdc recommends regular screening of all women under 25 for chlamydia even without any history or symptoms. Your best practice is barrier protection (condom) especially if in a casual relationship when abstinence is not an option.