We report measurements of the electrical resistivity and ac magnetic susceptibility of single crystalline LaPt$_2$Si$_2$ under pressure, in order to investigate the interplay of superconductivity and CDW order. LaPt$_2$Si$_2$ exhibits a first order phase transition from a tetragonal to orthorhombic structure, accompanied by the onset of CDW order below $T_{rm{CDW}}$ = 76 K, while superconductivity occurs at a lower temperature of $T_{rm{c}}$ = 1.87 K. We find that the application of pressure initially suppresses the CDW transition, but enhances $T_{rm{c}}$. At pressures above 2.4 GPa, CDW order vanishes, while both $T_{rm{c}}$ 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.
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