A quasiperiodic Pb monolayer has been formed on the fivefold surface of the Al-Pd-Mn quasicrystal. Growth of the monolayer proceeds via self-assembly of an interconnected network of pentagonal Pb stars, which are shown to be τ inflated compared to similar structural elements of the quasiperiodic substrate. Measurements of the electronic structure of the system using scanning tunneling spectroscopy and ultraviolet photoemission spectroscopy reveal that the Pb monolayer displays a pseudogap at the Fermi level which is directly related to its quasiperiodic structure.