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We present EventUPS, the first uncalibrated photometric stereo (UPS) method using an event camera--a neuromorphic sensor that asynchronously detects brightness changes with microsecond resolution. Traditional frame-based UPS methods are hindered by high bandwidth demands and limited use in dynamic scenes. These methods require dense image correspondence under varying illumination and are incompatible with the fundamentally different sensing paradigm of event data. Our approach introduces three key innovations: an augmented null space formulation that directly relates each event to joint constraints on surface normals and lighting, naturally handling ambient illumination; a continuous parameterization of time-varying illumination that connects asynchronous events to synchronized lighting estimation; and a lighting fixture with known relative geometry that reduces ambiguity to a convex-concave uncertainty. We validate EventUPS using a custom-built LED lighting system. Experimental results show that our method achieves accuracy surpassing its frame-based counterpart while requiring only 5% of the data bandwidth.