The family of La-based copper oxide sulfides includes LaCuOS, the prototypical transparent conducting oxide sulfide when doped, as well as , a compound with a layered structure analogous to LaCuOS but with a row of O atoms substituted by S atoms in the LaO layer. We propose that is an instance of an oxide-sulfide intrinsic transparent conductor (i.e., not requiring doping), while, so far, only oxides have been proposed as intrinsic transparent conductors. A one-dimensional (1D) atom chain as that found in often promotes in related systems a Peierls distortion with respect to the equispaced chain geometry, whereby adjacent atoms form dimers. Such a distortion is expected to open a band gap and lower the total energy, thus leading to thermodynamic stability. In we find that the configuration with undimerized 1D chains (the α phase) is both metallic and thermodynamically unstable. The fully dimerized, Peierls configurations (the β phase) exhibits an insulating band gap, however it is energetically unstable. The stable structure has chains with a degree of dimerization; in this structure the energetically preferred repeating chain motif is one in which two dimers are separated by one S atom, while chain segments with directly adjacent dimers are energetically unfavorable. The stable configuration is metallic with electron depletion in the layer with respect to the valence configuration that effectively amounts to creating a hole in the Cu bands at the valence maximum. In the stable partially dimerized phase the intraband, plasmonic transitions are weak while the onset of the strong interband transitions is at around 3 eV, which are both properties that enable transparency. In this paper we explain (i) why has an incomplete Peierls distortion, (ii) how the incomplete Peierls distortion in creates the coexistence of intrinsic transparency and conductivity which is otherwise unusual in oxide sulfides, and (iii) discuss the agreement between the predicted and the measured structure.