Understanding the suppression of ferroelectricity in perovskite thin films is a fundamental issue that has remained unresolved for decades. We report a synchrotron x-ray study of lead titanate as a function of temperature and film thickness for films as thin as a single unit cell. At room temperature, the ferroelectric phase is stable for thicknesses down to 3 unit cells (1.2 nanometers). Our results imply that no thickness limit is imposed on practical devices by an intrinsic ferroelectric size effect.