The explanation of the origin of microbialites and specifically stromatolitic structures is a problem of high relevance for decoding past sedimentary environments and deciphering the biogenicity of the oldest plausible remnants of life. We have investigated the morphogenesis of gypsum stromatolite-like structures currently growing in shallow ponds (puquíos) in the Salar de Llamara (Atacama Desert, Northern Chile). The crystal size, aspect ratio, and orientation distributions of gypsum crystals within the structures have been quantified and show indications for episodic nucleation and competitive growth of millimetric to centimetric selenite crystals into a radial, branched, and loosely cemented aggregate. The morphogenetical process is explained by the existence of a stable vertical salinity gradient in the ponds. Due to the non-linear dependency of gypsum solubility as a function of sodium chloride concentration, the salinity gradient produces undersaturated solutions, which dissolve gypsum crystals. This dissolution happens at a certain depth, narrowing the lower part of the structures, and producing their stromatolite-like morphology. We have tested this novel mechanism experimentally, simulating the effective dissolution of gypsum crystals in stratified ponds, thus providing a purely abiotic mechanism for these stromatolite-like structures.