Quantum critical points (QCPs), at which a second-order phase transition is continuously suppressed to zero temperature, are currently one of the central topics in solid-state physics. The strong interest emerges from observations of very unusual properties at QCPs such as the onset of unconventional superconductivity (SC). While QCPs found at the disappearance of magnetic order are quite common and intensively studied, a QCP that results from a structural transition is scarce and poorly investigated. Here, we report on the observation of a charge density wave (CDW) type of structural ordering in LuPt2In with a second-order transition at TCDW= 490 K. Substituting Pd for Pt suppresses TCDWcontinuously towards T = 0, leading to a QCP at 58% Pd substitution. We find a strong enhancement of bulk SC just at the QCP, pointing to a new type of interaction between CDW and SC.