Long House Valley, located in the Black Mesa area of northeastern Arizona (USA), was inhabited by the Kayenta Anasazi from circa 1800 B.C. to circa A.D. 1300. These people were prehistoric precursors of the modern Pueblo cultures of the Colorado Plateau. A rich paleoenvironmental record, based on alluvial geomorphology, palynology, and dendroclimatology, permits the accurate quantitative reconstruction of annual fluctuations in potential agricultural production (kg maize/hectare). The archaeological record of Anasazi farming groups from A.D. 200 to 1300 provides information on a millennium of sociocultural stasis, variability, change, and adaptation. We report on a multi-agent computational model of this society that closely reproduces the main features of its actual history, including population ebb and flow, changing spatial settlement patterns, and eventual rapid decline. The agents in the model are monoagriculturalists, who decide both where to situate their fields and where to locate their settlements.