The FlatDot detector has been used to demonstrate the separation of Cherenkov and scintillation light for 1 to 2MeV electrons in linear alkylbenzene (LAB). With an average PMT transit time spread (TTS) of 200ps, the early light in each event is clearly dominated by the Cherenkov signal, which on average comprises $86^{+2}_{-3}%$ of the light collected in the first 4.1ns of each event. The spatial distributions of the Cherenkov and scintillation light are found to match those predicted in Monte Carlo simulations. This is a key step towards demonstrating direction reconstruction of $beta$ decays, a technique that could reduce $^8$B solar neutrino backgrounds for neutrinoless double-beta decay experiments in liquid scintillator.