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Several efficient thermoelectric materials have been found among the ternary Zintl antimonides. If the band structure is highly asymmetric around the band gap, the efficiency as either n- or p-type may differ significantly. The Zintl antimonides have generally been found to be p-type. Surprisingly, this also holds true for the narrow band gap binary ZnSb and Zn4Sb3. Using ab initio calculations, we investigate intrinsic point defects in ZnSb as a possible origin of the p-type conductivity. Only Zn vacancies are found to be present in significant amounts at room temperature. The low formation energy of negatively charged Zn defects pins the electronic chemical potential to the lower part of the band gap leading to intrinsic ZnSb being ptype. We discuss this finding as a general explanation of p-type conductivity in Zintl antimonides, and how to overcome the doping limits in these materials.