Laminar membranes of two-dimensional materials are excellent candidates for applications in water filtration due to the formation of nanocapillaries between individual crystals that can exhibit a molecular and ionic sieving effect, while allowing high water flux. This approach has been exemplified previously with graphene oxide, however these membranes suffer from swelling when exposed to liquid water, leading to low salt rejection and reducing their applicability for desalination applications. Here, we demonstrate that by producing thin (~5 µm) laminar membranes of exfoliated molybdenum disulfide (MoS2) in a straightforward and scalable process, followed by a simple chemical functionalization step, we can efficiently reject (~99%) of the ions commonly found in sea water, while maintaining water fluxes significantly higher (~5 times) than those reported for graphene oxide membranes. These functionalized MoS2 membranes exhibit excellent long-term stability with no swelling, and consequent decrease in ion rejection, when immersed in water for periods exceeding 6 months. Similar stability is observed when exposed to organic solvents, indicating that they are ideal for a variety of technologically important filtration applications.