Covellite is a metallic layered mineral with rather strong interlayer interaction. Recently, synthesis of covellite nanosheets of 3.2 nm thickness was reported (Du et al 2012 Nat. Commun. 3 1177), which raises the question: 'What is the thinnest possible covellite nanosheet?' Based on density functional/plane waves calculations, we have shown that graphene-like structure CuS (1L-CuS) is unstable but can be stabilized on a support. Here, however, we demonstrate that the three layered CuS (3L-CuS) with thickness of 0.773 nm (including the atomic radius of the outer plans atoms) is predicted to be intrinsically stable, as confirmed by phonon analysis and Born-Oppenheimer molecular dynamics simulations, with 3L-CuS about 0.15 eV per CuS less stable than the bulk. Interestingly, the electronic band structure shows metallic character with four bands crossing the Fermi level. The nature of chemical bonding is confirmed by a detailed topological analysis of the electron density.