I am in a monogamous relationship, am I safe from chlamydia?

Maybe, maybe not. Two people in a monogamous relationship must both start out free of chlamydia. That means "the couple" is chlamydia-free. Then, each partner must stay monogamous in order for chlamydia to not enter the couple's relationship by way of a third party.
Thanks for asking! Monogamous relationship does not gaurantee anyone from not getting chlamydia. If either of you have been in a relationship before which involved sex need evaluated for std. Remember chlamydia can be asymptomatic.