Iron selenide superconductors exhibit a number of unique characteristics that are helpful for understanding the mechanism of superconductivity in high-Tc iron-based superconductors more generally. However, in the case of AxFe2Se2 (A = K, Rb, Cs), the presence of an intergrown antiferromagnetic insulating phase makes the study of the underlying physics problematic. Moreover, FeSe-based systems intercalated with alkali metal ions, NH3 molecules or organic molecules are extremely sensitive to air, which prevents the further investigation of their physical properties. It is therefore desirable to find a stable and easily accessible FeSe-based superconductor to study its physical properties in detail. Here, we report the synthesis of an air-stable material, (Li0.8Fe0.2)OHFeSe, which remains superconducting at temperatures up to ~40 K, by means of a novel hydrothermal method. The crystal structure is unambiguously determined by a combination of X-ray and neutron powder diffraction and nuclear magnetic resonance. Moreover, antiferromagnetic order is shown to coexist with superconductivity. This synthetic route opens a path for exploring superconductivity in other related systems, and confirms the appeal of iron selenides as a platform for understanding superconductivity in iron pnictides more broadly.