On a new limit theorem in probability theory (Translation of 'Sur un nouveau th\'eor\`eme-limite de la th\'eorie des probabilit\'es')

This is a translation of Harald Cram'er’s article, ‘On a new limit theorem in probability theory’, published in French in 1938 and deriving what is considered by mathematicians to be the first large deviation result. My hope is that this translation will help disseminate this historically important work, 80 years after its publication.