We present EventUPS, the first uncalibrated photometric stereo method using event cameras—neuromorphic sensors that asynchronously detect brightness changes with microsecond resolution. Frame-based uncalibrated photometric stereo methods imposed high bandwidth demands and limiting applicability in dynamic scenes. They require dense image correspondence under varying illumination, cannot be directly applicable due to event data due to their fundamentally different sensing paradigm. Our approach introduces three key innovations: i) an augmented null space formulation that directly relates each event to constraints on surface normals and lighting, naturally handling ambient illumination; ii) a continuous parameterization of time-varying illumination that bridges asynchronous events to synchronized lighting estimation; iii) a structured lighting approach with known relative geometry that resolves the ambiguity to merely convex-concave uncertainty. We validate EventUPS using a custom-built LED-based lighting system implementing dual-ring and trefoil curve patterns. Extensive experiments on synthetic, semi-real, and real data demonstrate that our method achieves accuracy surpassing frame-based counterpart while requiring only 5\% of the data bandwidth.