  We suggest that Cobalt-Oxychalcogenide layers constructed by vertex sharing
CoA$_2$O$_2$ (A=S,Se,Te) tetrahedra, such as BaCoAO, are strongly correlated
multi-orbital electron systems that can provide important clues on the cause of
unconventional superconductivity. Differing from cuprates and iron-based
superconductors, these systems lack of the C$_4$ rotational symmetry. However,
their parental compounds possess antiferromagnetic(AFM) Mott insulating states
through pure superexchange interactions and the low energy physics near Fermi
surfaces upon doping is also attributed mainly to the three t$_{2g}$ orbitals
that dominate the AFM interactions. We derive a low energy effective model for
these systems and predict that a d-wave-like superconducting state with
reasonable high transition temperature can emerge by suppressing the AFM
ordering even if the pairing symmetry can not be classified by the rotational
symmetry any more.
