© 2019 Association for Computing Machinery. In underlay coexistence, secondary users (SUs) attempt to keep their interference to the primary users (PUs) under a threshold. Due to the absence of cooperation from the PUs, there exists much uncertainty at the SUs in terms of channel state information (CSI). An effective approach to cope such uncertainty is to introduce occasional interference threshold violation by the SUs, as long as such occasional violation can be tolerated by the PUs. This paper exploits this idea through a chance constrained programming (CCP) formulation, where the knowledge of uncertain CSI is limited to only the first and second order statistics rather than its complete distribution information. Our main contribution is the introduction of a novel and powerful technique, called Exact Conic Reformulation (ECR), to reformulate the intractable chance constraints. ECR guarantees an equivalent reformulation for linear chance constraints into deterministic conic constraints and does not suffer from the limitations associated with the state-of-the-art approach – Bernstein Approximation. Simulation results confirm that ECR offers significant performance improvement over Bernstein Approximation in uncorrelated channels and a competitive solution in correlated channels (where Bernstein Approximation is no longer applicable).