Quasicrystals, materials with aperiodic long-range order, have been found in intermetallics, soft materials such as colloids and supermolecules, and also in two-dimensional monolayer films. Here we present the first example of three-dimensional growth of a single-element quasicrystalline film. Using a hitherto unexplored template, the icosahedral Ag-In-Yb quasicrystal, and various experimental techniques combined with theoretical calculations of adsorption energies, we find that lead atoms deposited on the surface occupy the positions of atoms in the rhombic triacontahedral cluster, the building block of the substrate, and thus grow in layers with different heights and adsorption energies. We show that the adlayer-adlayer interaction is crucial for stabilizing this epitaxial quasicrystalline structure. The finding opens an avenue for further investigation of the impact of the aperiodic atomic order over periodic order on the physical and chemical properties of materials.