CaCoSO, synthesized from CaO, Co, and S at 900 degrees C, is isostructural with CaZnSO and CaFeSO. The structure is non-centrosymmetric by virtue of the arrangement of the vertex-sharing CoS3O tetrahedra which are linked by their sulfide vertices to form layers. The crystal structure adopts space group P6(3)mc (No. 186), and the lattice parameters are a = 3.7524(9) angstrom and c = 11.138(3) angstrom at room temperature with two formula units in the unit cell. The compound is highly insulating, and powder neutron diffraction measurements reveal long-range antiferromagnetic order with a propagation vector k = (1/3, 1/3, 1/2). The magnetic scattering from a powder sample can be modeled starting from a 120 degrees arrangement of Co2+ spin vectors in the triangular planes and then applying a canting out of the planes which can be modeled in the magnetic space group C(c)c (space group 9.40 in the Belov, Neronova, and Smirnova (BNS) scheme) with Co2+ moments of 2.72(5) mu(B). The antiferromagnetic structure of the recently reported compound BaCoSO, which has a very different crystal structure from CaCoSO, is also described, and this magnetic structure and the magnitude of the ordered moment (2.75(2) mu(B)) are found by experiment to be similar to those predicted computationally.