Emissive PbS/CdS core/shell nanosheets are synthesized using a cation-exchange method. A significant blue-shift of the photoluminescence is observed, indicating a stronger quantum confinement in the PbS core as its thickness is reduced. High resolution transmission-electron-microscopy images of the cross sections of the core/shell nanosheets show atomically sharp interfaces between PbS and CdS. Accurate analysis of the thickness of each layer reveals the relationship between the energy gap and the thickness in the extremely one-dimensionally confined nanostructure. Photoluminescence lifetime of the core/shell nanosheets is significantly longer than the core-only nanosheets, indicating better surface passivation.