The eradication of nonnative plant pathogens is a key challenge in plant disease epidemiology. Asiatic citrus canker is an economically significant disease of citrus caused by the bacterial plant pathogen Xanthomonas citri subsp. citri. The pathogen is a major exotic disease problem in many citrus producing areas of the world including the United States, Brazil, and Australia. Various eradication attempts have been made on the disease but have been associated with significant social and economic costs due to the necessary removal of large numbers of host trees. In this paper, a spatially explicit stochastic simulation model of Asiatic citrus canker is introduced that describes an epidemic of the disease in a heterogeneous host landscape. We show that an optimum eradication strategy can be determined that minimizes the adverse costs associated with eradication. In particular, we show how the optimum strategy and its total cost depend on the topological arrangement of the host landscape. We discuss the implications of the results for invading plant disease epidemics in general and for historical and future eradication attempts on Asiatic citrus canker.