Here we report prediction of two new ternary chalcogenides that can potentially be used as p-type transparent conductors along with experimental synthesis and initial characterization of these previously unknown compounds, Cs2Zn3Ch4 (Ch = Se, Te). In particular, the structures are predicted based on density functional calculations and confirmed by experiments. Phase diagrams, electronic structure, optical properties, and defect properties of Cs2Zn3Se4 and Cs2Zn3Te4 are calculated to assess the viability of these materials as p-type TCMs. Cs2Zn3Se4 and Cs2Zn3Te4, which are stable under ambient air, display large optical band gaps (calculated to be 3.61 and 2.83 eV, respectively) and have small hole effective masses (0.5-0.77 me) that compare favorably with other proposed p-type TCMs. Defect calculations show that undoped Cs2Zn3Se4 and Cs2Zn3Te4 are p-type materials. However, the free hole concentration may be limited by low-energy native donor defects, e.g., Zn interstitials. Lastly, non-equilibrium growth techniques should be useful for suppressing the formation of native donor defects, thereby increasing the hole concentration.