ProtonMail is an online email service that claims to offer end-to-end encryption such that "even [ProtonMail] cannot read and decrypt [user] emails." The service, based in Switzerland, offers email access via webmail and smartphone applications to over five million users as of November 2018. In this work, we provide the first independent analysis of ProtonMail's cryptographic architecture. We find that for the majority of ProtonMail users, no end-to-end encryption guarantees have ever been provided by the ProtonMail service and that the "Zero-Knowledge Password Proofs" are negated by the service itself. We also find and document weaknesses in ProtonMail's "Encrypt-to-Outside" feature. We justify our findings against well-defined security goals and conclude with recommendations.