The structural and dynamic properties of the mineral Cooperite (PtS) are investigated using density-functional theory. The results show that a competition with the less symmetric but more compact PdS structure leads to a phase transition when the pressure is increased. However, before the phase transition, PtS displays a rare anomalous elastic behavior by expanding along its long axis under hydrostatic pressure. We report the elastic constants of PtS and interpret this negative linear compressibility in the context of a displacive phase transition. We also show that the real structure of PtS is less symmetric than originally determined by experiment.