The Suzaku AGN Spin Survey is designed to determine the supermassive black hole spin in six nearby active galactic nuclei (AGN) via deep Suzaku stares, thereby giving us our first glimpse of the local black hole spin distribution. Here, we present an analysis of the first target to be studied under the auspices of this Key Project, the Seyfert galaxy NGC 3783. Despite complexity in the spectrum arising from a multi-component warm absorber, we detect and study relativistic reflection from the inner accretion disk. Assuming that the X-ray reflection is from the surface of a flat disk around a Kerr black hole, and that no X-ray reflection occurs within the general relativistic radius of marginal stability, we determine a lower limit on the black hole spin of a > 0.88 (99% confidence). We examine the robustness of this result to the assumption of the analysis, and present a brief discussion of spin-related selection biases that might affect flux-limited samples of AGN.
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