Borexino is a 280 t liquid scintillator detector at the Laboratori Nazionali del Gran Sasso (LNGS), Italy. Its main goal is the precision spectroscopy of solar neutrinos down to energies of 0.19 MeV and for this task it features an unprecedented radio-purity and a high scintillation light yield. The solar neutrinos are measured by the elastic scattering off electrons which induce isotropically emitted scintillation photons as well as a sub-dominant number of Cherenkov photons that are detected by photomulitplier tubes. Here we present the first detection of sub-MeV solar neutrinos using their associated Cherenkov photons in a high light yield liquid scintillator detector. In Borexino electrons with E>0.16 MeV produce Cherenkov photons, where the ratio of Cherenkov photons from the neutrino scattered electrons is estimated to be < 1% for all PMT hits, so a typical event by event direction reconstruction is not possible. Instead this analysis looks at the integrated signal of the PMT hits of all detected events by correlating the position of each hit PMT relative to the reconstructed position of the event and the well known position of the Sun. In this way it is possible to measure an angular distribution that shows the statistical contribution of Cherenkov photons from the solar neutrino recoil electrons. Using the Geant4-based Borexino Monte Carlo to produce the expected angular distribution for solar neutrinos and background we have measured 8643⁺²²⁵²₋₂₀₅₈ neutrino events out of 19904 total events for an energy region around the ⁷Be edge between 0.53 MeV and 0.74 MeV.