The spindle checkpoint prevents chromosome loss by preventing chromosome segregation in cells with improperly attached chromosomes [1, 2 and 3]. The checkpoint senses defects in the attachment of chromosomes to the mitotic spindle  and the tension exerted on chromosomes by spindle forces in mitosis [5, 6 and 7]. Because many cancers have defects in chromosome segregation, this checkpoint may be required for survival of tumor cells and may be a target for chemotherapy. We performed a phenotype-based chemical-genetic screen in budding yeast and identified an inhibitor of the spindle checkpoint, called cincreasin. We used a genome-wide collection of yeast gene-deletion strains and traditional genetic and biochemical analysis to show that the target of cincreasin is Mps1, a protein kinase required for checkpoint function . Despite the requirement for Mps1 for sensing both the lack of microtubule attachment and tension at kinetochores, we find concentrations of cincreasin that selectively inhibit the tension-sensitive branch of the spindle checkpoint. At these concentrations, cincreasin causes lethal chromosome missegregation in mutants that display chromosomal instability. Our results demonstrate that Mps1 can be exploited as a target and that inhibiting the tension-sensitive branch of the spindle checkpoint may be a way of selectively killing cancer cells that display chromosomal instability.