Yb ₁₄ MnSb ₁₁ and Yb ₁₄ MgSb ₁₁ are among the best p-type high-temperature (>1200 K) thermoelectric materials, yet other compounds of this Ca ₁₄ AlSb ₁₁ structure type have not matched their stability and efficiency. First-principles computations show that the features in the electronic structures that have been identified to lead to high thermoelectric performances are present in Yb ₁₄ ZnSb ₁₁ , which has been presumed to be a poor thermoelectric material. We show that the previously reported low power factor of Yb ₁₄ ZnSb ₁₁ is not intrinsic and is due to the presence of a Yb ₉ Zn _{4+ x} Sb ₉ impurity uniquely present in the Zn system. Phase-pure Yb ₁₄ ZnSb ₁₁ synthesized through a route avoiding the impurity formation reveals its exceptional high-temperature thermoelectric properties, reaching a peak zT of 1.2 at 1175 K. Beyond Yb ₁₄ ZnSb ₁₁ , the favorable band structure features for thermoelectric performance are universal among the Ca ₁₄ AlSb ₁₁ structure type, opening the possibility for high-performance thermoelectric materials.