Realization of an elemental solid-state quasicrystal has remained a distant dream so far in spite of extensive work in this direction for almost two decades. In the present work, we report the discovery of quasiperiodic ordering in a thick layer of elemental Sn grown on icosahedral (i)-Al-Pd-Mn. The scanning tunneling microscopy (STM) images and the low-energy electron diffraction patterns of the Sn layer show specific structural signatures that portray quasiperiodicity but are distinct from the substrate. Photoemission spectroscopy reveals the existence of the pseudogap around the Fermi energy up to the maximal Sn thickness. The structure of the Sn layer is modeled as a form of quasicrystalline clathrate on the basis of multiple supporting evidences: First, from ab initio total energy evaluation, the energy of bulk Sn clathrate quasicrystal is lower than the high-temperature metallic β-Sn phase, but higher than the low-temperature α-Sn phase. A comparative study of the free slab energetics shows that surface energy favors clathrate over α-Sn up to about 4-nm layer thickness and matches β-Sn for narrow window of slab thickness of 2–3 nm. Second, the bulk clathrate exhibits gap opening near Fermi energy, while the free slab form exhibits a pronounced pseudogap, which explains the pseudogap observed in photoemission. Third, the STM images exhibit good agreement with clathrate model. Finally, we establish the adlayer-substrate compatibility based on very similar (within 1%) the cage-cage separation in the Sn clathrate and the pseudo-Mackay cluster-cluster separation on the i-Al-Pd-Mn surface. Furthermore, the nucleation centers of the Sn adlayer on the substrate are identified and these are shown to be a valid part of the Sn clathrate structure. Thus, based on both experimental and ab initio density functional theory calculations, we propose that 4-nm-thick Sn adlayer deposited on fivefold surface of i-Al-Pd-Mn substrate is in fact a metastable realization of elemental, clathrate family quasicrystal.