Well, for starters, you'd think someone with Chalmydia would have learned the hard way that latex barriers are a good idea: for vaginal, anal and/or oral sex, at a minimum. So, unless a couple has been practicing all aspects of safer sex monogamously for six motnhs, we'd advise partners use a dental dam during cunnilingus.
As well, someone currently being treated for any STI should abstain from partnered sex until the treatment is finished.
Per chlamydia specifically, it is a genital infection, not an oral infection, though in rare cases, it can infect the eyes.
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