I present a new focal-plane analog VLSI sensor that estimates optical flow in two visual dimensions. The chip significantly improves previous approaches both with respect to the applied model of optical flow estimation as well as the actual hardware implementation. Its distributed computational architecture consists of a network of locally connected motion units that collectively estimate the optimal optical flow field. The novel gradient-based motion mode assumes visual motion to be translational, smooth and biased. The model guarantees that the estimation problem is computationally well-posed regardless of the visual input. Model parameters can be globally adjusted, leading to a rich output behavior. Varying the smoothness strength, for example, can provide a continuous spectrum of motion estimates, ranging from normal to global optical flow. Unlike approaches that rely on the explicit matching of brightness edges in space or time, the applied gradient-based model assures spatiotemporal continuity on visual information. The non-linear network conductances improve the resulting optical flow estimate because they reduce spatial smoothing across large velocity differences and minimize the bias for reliable stimuli. Extended measurements of a 30x30 array prototype sensor under real-world conditions demonstrate the validity of the model and the robustness and functionality of the implementation.