Despite the fact there is a plethora of magnetic delafossite compounds in the bulk polycrystalline phase, so far, only a few of them have been fabricated as thin films. The challenges in the fabrication of delafossite thin films are imposed by the phase purity and stability of the composition related with the preparation conditions. Here we report the growth of a new delafossite thin film, a sodium iron oxide of the beta-NaFeO2 phase, grown on a ZnO seed layer by pulsed laser deposition, using as target a single phase polycrystalline powder of beta-NaFeO2. The purity of the thin films has been verified with X-ray diffraction, Scanning electron and Atomic Force Microscopy as well as Fourier Transform Infrared Spectroscopy. The crucial parameter for the growth of the thin films has been the partial oxygen pressure, as the beta-NaFeO2 is obtained at 2 Pa. Applying higher or lower pressures resulted in the formation the hematite and maghemite iron oxides as secondary phases, as indicated by X-ray diffraction patterns. SEM and AFM studies confirm a good two dimensional growth for the pure phase beta-NaFeO2, whereas FT-IR measurements revealed characteristic beta-NaFeO2 bands.