We report measurements of the electrical resistivity and ac magnetic susceptibility of single crystalline LaPt2Si2 under pressure, in order to investigate the interplay of superconductivity and CDW order. LaPt2Si2 exhibits a first order phase transition from a tetragonal to orthorhombic structure, accompanied by the onset of CDW order below TCDW = 76 K, while superconductivity occurs at a lower temperature of Tc = 1.87 K. We find that the application of pressure initially suppresses the CDW transition, but enhances Tc. At pressures above 2.4 GPa, CDW order vanishes, while both Tc and the resistivity A-coefficient reach a maximum value around this pressure. Our results suggest that the occurrence of a superconducting dome can be accounted for within the framework of BCS theory, where there is a maximum in the density of states upon the closure of the CDW gap.