Conflict is an essential element of interesting stories, but little research in computer narrative has addressed it directly. We present a model of narrative conflict inspired by narratology research and based on Partial Order Causal Link (POCL) planning. This model informs an algorithm called CPOCL which extends previous research in story generation. Rather than eliminate all threatened causal links, CPOCL marks certain steps in a plan as non-executed in order to preserve the conflicting subplans of all characters without damaging the causal soundness of the overall story.