We present a procedure to grow thin films of lead sulfide (PbS) with 'solution Atomic Layer Deposition' (sALD), a technique which transfers the principles of ALD from the gas phase (gALD) to liquid processing. PbS thin films are successfully deposited on planar and porous substrates with a procedure that exhibits the unique ALD characteristics of self-limiting surface chemistry and linear growth at room temperature. The polycrystalline p-type PbS films are stoichiometric and pure. They are converted to the hybrid perovskite methylammonium iodoplumbate (methylammonium lead iodide, MAPI, CH₃NH₃PbI₃) by annealing to 150 °C in the presence of vapors from methylammonium iodide (MAI).