Health care data repositories play an important role in driving progress in medical research. Finding new pathways to discovery requires having adequate data and relevant analysis. However, it is critical to ensure the privacy and security of the stored data. In this paper, we identify a dangerous inference attack against naive suppression based approaches that are used to protect sensitive information. We base our attack on the querying system provided by the Healthcare Cost and Utilization Project, though it applies in general to any medical database providing a query capability. We also discuss potential solutions to this problem.