Large array-based transmission uses the combination of a massive number of antenna elements and clever precoder designs to achieve array gain and spatially multiplex different users. These precoders require linear front-ends, and more specifically linear power amplifiers (PAs). However, this reduces energy efficiency since PAs are most efficient close to saturation, where they generate most nonlinear distortion. Moreover, the use of conventional precoders, such as \gls{mrt}, induces a coherent combining of distortion at the user location, degrading the signal quality. In this work, a linear precoder is proposed that allows working close to saturation while canceling the coherent combining of the third order nonlinear \gls{pa} distortion at the user location. In contrast to other solutions, the zero third-order distortion (Z3RO) precoder does not require prior knowledge of the signal statistics and the PA model. The design consists of saturating a single or a few antennas on purpose together with an opposite phase shift to compensate for the distortion of all other antennas. The resulting array gain penalty becomes negligible as the number of base station antennas grows large.