We report on the successful synthesis of highly conductive PdCoO2 ultrathin films on Al2O3 (0001) by pulsed laser deposition. The thin films grow along the c-axis of the layered delafossite structure of PdCoO2, corresponding to the alternating stacking of conductive Pd layers and CoO2 octahedra. The thickness-dependent transport measurement reveals that each Pd layer has a homogeneous sheet conductance as high as 5.5 mS in the samples thicker than the critical thickness of 2.1 nm. Even at the critical thickness, high conductivity exceeding 104 Scm-1 is achieved. Optical transmittance spectra exhibit high optical transparency of PdCoO2 thin films particularly in the near-infrared region. The concomitant high values of electrical conductivity and optical transmittance make PdCoO2 ultrathin films as promising transparent electrodes for triangular-lattice-based materials.