We present the Multilingual TEDx corpus, built to support speech recognition (ASR) and speech translation (ST) research across many non-English source languages. The corpus is a collection of audio recordings from TEDx talks in 8 source languages. We segment transcripts into sentences and align them to the source-language audio and target-language translations. The corpus is released along with open-sourced code enabling extension to new talks and languages as they become available. Our corpus creation methodology can be applied to more languages than previous work, and creates multi-way parallel evaluation sets. We provide baselines in multiple ASR and ST settings, including multilingual models to improve translation performance for low-resource language pairs.