Distributed computation of Voronoi cells in sensor networks, i.e. computing the locus of points in a sensor field closest to a given sensor, is a key building block that supports a number of applications in both the data and control planes. For example, knowledge of Voronoi cells facilitates efficient methods for computing the piece-wise approximation of a field, whereby each sensor acts as a representative for the set of points in its Voronoi cell; awareness of Voronoi boundaries and Voronoi neighbors is also useful in load balancing and energy conservation. The methods currently advocated for distributed Voronoi computation in sensor networks are heuristic approximations that can introduce significant inaccuracies that are difficult to rigorously quantify; we demonstrate that these methods may err by a factor of 5 or more in some circumstances. We present and prove an exact method which eliminates these inaccuracies, at the cost of increased messaging overhead, but without necessitating contact with the entire network. To our knowledge, this is the first distributed algorithm that computes accurate Voronoi cells without requiring all-to-all communication. We implement it as a TinyOS module and quantitatively analyze its performance.