  For reasonable parameters a hole bound to a Na^{+} acceptor in
Ca_{2-x}Na_{x}CuO_{2}Cl_{2} has a doubly degenerate ground state whose
components can be represented as states with even (odd) reflection symmetry
around the x(y) -axes. The conductance pattern for one state is anisotropic as
the tip of a tunneling microscope scans above the Cu-O-Cu bonds along the
x(y)-axes. This anisotropy is pronounced at lower voltages but is reduced at
higher voltages. Qualitative agreement with recent experiments leads us to
propose this effect as an explanation of the broken local rotational symmetry.
