Misfit-layered (ML) cobalt oxides of the general formula of [MmA2Om+2]qCoO2 have been proven to be efficient thermoelectric materials as the structure is capable in accommodating the two seemingly contradictory characteristics of high electrical conductivity and large thermo-electric power. They are also potential hosts for other oxymoron-like functions. The known phases all contain one or two square-planar MO (M = Co, Bi, Pb, Tl, etc.) layers sandwiched together with AO (A = Ca, Sr, Ba, etc.) planes of square symmetry and CoO2 layers of hexagonal symmetry. Here we report realization of the simplest (m = 0) ML phase forming in the Sr-Co-O system with the cation ratio, Sr/Co = 1. Atomic-resolution TEM imaging confirms for the new phase the parent three-layer crystal structure, SrO-SrO-CoO2, which is compatible with the formula of [Sr2O2]qCoO2. Electron diffraction reveals that the phase is rather commensurate, i.e. the misfit parameter q is 0.5. Nevertheless, in terms of the transport-property characteristics the new ML parent is comparable to its earlier-established and more complex derivatives.