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 \geq 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 .