The CRESST experiment is a direct dark matter search which aims to measure interactions of potential dark matter particles in an Earth-bound detector. With the current stage, CRESST-III, we focus on a low energy threshold for increased sensitivity towards light dark matter particles. In this paper we describe the analysis of one detector operated in the first run of CRESST-III (05/2016–02/2018) achieving a nuclear recoil threshold of 30.1 eV. This result was obtained with a 23.6 g crystal operated as a cryogenic scintillating calorimeter in the CRESST setup at the Laboratori Nazionali del Gran Sasso (LNGS). Both the primary phonon (heat) signal and the simultaneously emitted scintillation light, which is absorbed in a separate silicon-on-sapphire light absorber, are measured with highly sensitive transition edge sensors operated at . The unique combination of these sensors with the light element oxygen present in our target yields sensitivity to dark matter particle masses as low as .