theoretically it guess it would be possible if the towel was still wet from chlamydia and you wiped a very sensitive area but why would you be using someone's wet towel? chlamydia is a sexually-transmitted disease and in overwhelming number of cases this is the only way that it spreads. babies can get chlamydia in their eyes if mother had it in her vagina during delivery but otherwise people tend to get chlamydia the old fashioned way - through sexual contact.
can you get chlamydia by using someone towel that is infected with chlyamydia?