In the past few years, the study of exoplanets has evolved from being pure discovery, then being more exploratory in nature and finally becoming very quantitative. In particular, transmission spectroscopy now allows the study of exoplanetary atmospheres. Such studies rely heavily on space-based or large ground-based facilities, because one needs to perform time-resolved, high signal-to-noise spectroscopy. The very recent exchange of the prisms of the FORS2 atmospheric diffraction corrector on ESOs Very Large Telescope should allow us to reach higher data quality than was ever possible before. With FORS2, we have obtained the first optical ground-based transmission spectrum of WASP-19b, with 20 nm resolution in the 550--830 nm range. For this planet, the data set represents the highest resolution transmission spectrum obtained to date. We detect large deviations from planetary atmospheric models in the transmission spectrum redwards of 790 nm, indicating either additional sources of opacity not included in the current atmospheric models for WASP-19b or additional, unexplored sources of systematics. Nonetheless, this work shows the new potential of FORS2 for studying the atmospheres of exoplanets in greater detail than has been possible so far.