DNA-damaging chemotherapeutics are widely used in cancer treatments, but for solid tumors they often leave a residual tumor-cell population. Here we investigated how cellular states might affect the response of individual cells in a clonal population to cisplatin, a DNA-damaging chemotherapeutic agent. Using a live-cell reporter of cell cycle phase and long-term imaging, we monitored single-cell proliferation before, at the time of, and after treatment. We found that in response to cisplatin, cells either arrested or died, and the ratio of these outcomes depended on the dose. While we found that the cell cycle phase at the time of cisplatin addition was not predictive of outcome, the proliferative history of the cell was: highly proliferative cells were more likely to arrest than to die, whereas slowly proliferating cells showed a higher probability of death. Information theory analysis revealed that the dose of cisplatin had the greatest influence on the cells' decisions to arrest or die, and that the proliferation status interacted with the cisplatin dose to further guide this decision. These results show an unexpected effect of proliferation status in regulating responses to cisplatin and suggest that slowly proliferating cells within tumors may be acutely vulnerable to chemotherapy.