The discovery of quasicrystals--crystalline structures that show order while lacking periodicity--forced a paradigm shift in crystallography. Initially limited to intermetallic systems, the observation of quasicrystalline structures has recently expanded to include 'soft' quasicrystals in the fields of colloidal and supermolecular chemistry. Here we report an aperiodic oxide that grows as a two-dimensional quasicrystal on a periodic single-element substrate. On a Pt(111) substrate with 3-fold symmetry, the perovskite barium titanate BaTiO3 forms a high-temperature interface-driven structure with 12-fold symmetry. The building blocks of this dodecagonal structure assemble with the theoretically predicted Stampfli-Gähler tiling having a fundamental length-scale of 0.69 nm. This example of interface-driven formation of ultrathin quasicrystals from a typical periodic perovskite oxide potentially extends the quasicrystal concept to a broader range of materials. In addition, it demonstrates that frustration at the interface between two periodic materials can drive a thin film into an aperiodic quasicrystalline phase, as proposed previously. Such structures might also find use as ultrathin buffer layers for the accommodation of large lattice mismatches in conventional epitaxy.