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The wide adoption and application of Masked language models (MLMs) on sensitive data (from legal to medical) necessitates a thorough quantitative investigation into their privacy vulnerabilities -to what extent do MLMs leak information about their training data? Prior attempts at measuring leakage of MLMs via membership inference attacks have been inconclusive, implying potential robustness of MLMs to privacy attacks. In this work, we posit that prior attempts were inconclusive because they based their attack solely on the MLM's model score. We devise a stronger membership inference attack based on likelihood ratio hypothesis testing that involves an additional reference MLM to more accurately quantify the privacy risks of memorization in MLMs. We show that masked language models are extremely susceptible to likelihood ratio membership inference attacks: Our empirical results, on models trained on medical notes, show that our attack improves the AUC of prior membership inference attacks from 0.66 to an alarmingly high 0.90 level, with a significant improvement in the low-error region: at 1% false positive rate, our attack is 51× more powerful than prior work.