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We report a characterization of surfaces of the dichalcogenide TaSe using scanning tunneling microscopy and spectroscopy (STM/S) at 150 mK. When the top layer has the 2H structure and the layer immediately below the 1T structure, we find a singular spatial dependence of the tunneling conductance below 1 K, changing from a zero bias peak on top of Se atoms to a gap in between Se atoms. The zero bias peak is additionally modulated by the commensurate $3a_0 \times 3a_0_2_2$ show a spatially homogeneous superconducting gap with a critical temperature also of 1 K. We discuss possible origins for the peculiar tunneling conductance in single layers.

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