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Event cameras offer a considerable alternative to RGB cameras in many scenarios. While there are recent works on event-based novel-view synthesis, dense 3D mesh reconstruction remains scarcely explored and existing event-based techniques are severely limited in their 3D reconstruction accuracy. To address this limitation, we present EventNeuS, a self-supervised neural model for learning 3D representations from monocular colour event streams. Our approach, for the first time, combines 3D signed distance function and density field learning with event-based supervision. Furthermore, we introduce spherical harmonics encodings into our model for enhanced handling of view-dependent effects. EventNeuS outperforms existing approaches by a significant margin, achieving 34% lower Chamfer distance and 31% lower mean absolute error on average compared to the best previous method.